diff --git a/numpy/core/src/multiarray/arrayobject.c b/numpy/core/src/multiarray/arrayobject.c
index 1b197d0f246b..f99de2a39b4f 100644
--- a/numpy/core/src/multiarray/arrayobject.c
+++ b/numpy/core/src/multiarray/arrayobject.c
@@ -493,14 +493,6 @@ array_dealloc(PyArrayObject *self)
         if (PyDataType_FLAGCHK(fa->descr, NPY_ITEM_REFCOUNT)) {
             PyArray_XDECREF(self);
         }
-        /*
-         * Allocation will never be 0, see comment in ctors.c
-         * line 820
-         */
-        size_t nbytes = PyArray_NBYTES(self);
-        if (nbytes == 0) {
-            nbytes = fa->descr->elsize ? fa->descr->elsize : 1;
-        }
         if (fa->mem_handler == NULL) {
             char *env = getenv("NUMPY_WARN_IF_NO_MEM_POLICY");
             if ((env != NULL) && (strncmp(env, "1", 1) == 0)) {
@@ -511,7 +503,16 @@ array_dealloc(PyArrayObject *self)
             }
             // Guess at malloc/free ???
             free(fa->data);
-        } else {
+        }
+        else {
+            /*
+             * In theory `PyArray_NBYTES_ALLOCATED`, but differs somewhere?
+             * So instead just use the knowledge that 0 is impossible.
+             */
+            size_t nbytes = PyArray_NBYTES(self);
+            if (nbytes == 0) {
+                nbytes = 1;
+            }
             PyDataMem_UserFREE(fa->data, nbytes, fa->mem_handler);
             Py_DECREF(fa->mem_handler);
         }
diff --git a/numpy/core/src/multiarray/common.h b/numpy/core/src/multiarray/common.h
index b3526c4c1de2..85fd3aab1f40 100644
--- a/numpy/core/src/multiarray/common.h
+++ b/numpy/core/src/multiarray/common.h
@@ -292,6 +292,35 @@ npy_memchr(char * haystack, char needle,
     return p;
 }
 
+/*
+ * Helper to work around issues with the allocation strategy currently
+ * allocating not 1 byte for empty arrays, but enough for an array where
+ * all 0 dimensions are replaced with size 1 (if the itemsize is not 0).
+ *
+ * This means that we can fill in nice (nonzero) strides and still handle
+ * slicing direct math without being in danger of leaving the allocated byte
+ * bounds.
+ * In practice, that probably does not matter, but in principle this would be
+ * undefined behaviour in C.  Another solution may be to force the strides
+ * to 0 in these cases.  See also gh-15788.
+ *
+ * Unlike the code in `PyArray_NewFromDescr` does no overflow checks.
+ */
+static NPY_INLINE npy_intp
+PyArray_NBYTES_ALLOCATED(PyArrayObject *arr)
+{
+    if (PyArray_ITEMSIZE(arr) == 0) {
+        return 1;
+    }
+    npy_intp nbytes = PyArray_ITEMSIZE(arr);
+    for (int i = 0; i < PyArray_NDIM(arr); i++) {
+        if (PyArray_DIMS(arr)[i] != 0) {
+            nbytes *= PyArray_DIMS(arr)[i];
+        }
+    }
+    return nbytes;
+}
+
 
 /*
  * Simple helper to create a tuple from an array of items. The `make_null_none`
diff --git a/numpy/core/src/multiarray/ctors.c b/numpy/core/src/multiarray/ctors.c
index e22708f39650..78003306afe9 100644
--- a/numpy/core/src/multiarray/ctors.c
+++ b/numpy/core/src/multiarray/ctors.c
@@ -754,14 +754,20 @@ PyArray_NewFromDescr_int(
         }
         fa->strides = fa->dimensions + nd;
 
-        /* Copy dimensions, check them, and find total array size `nbytes` */
+        /*
+         * Copy dimensions, check them, and find total array size `nbytes`
+         *
+         * Note that we ignore 0-length dimensions, to match this in the `free`
+         * calls, `PyArray_NBYTES_ALLOCATED` is a private helper matching this
+         * behaviour, but without overflow checking.
+         */
         for (int i = 0; i < nd; i++) {
             fa->dimensions[i] = dims[i];
 
             if (fa->dimensions[i] == 0) {
                 /*
                  * Compare to PyArray_OverflowMultiplyList that
-                 * returns 0 in this case.
+                 * returns 0 in this case. See also `PyArray_NBYTES_ALLOCATED`.
                  */
                 continue;
             }
diff --git a/numpy/core/src/multiarray/getset.c b/numpy/core/src/multiarray/getset.c
index 2544ca9e7301..a92ac44b7846 100644
--- a/numpy/core/src/multiarray/getset.c
+++ b/numpy/core/src/multiarray/getset.c
@@ -384,15 +384,7 @@ array_data_set(PyArrayObject *self, PyObject *op, void *NPY_UNUSED(ignored))
     }
     if (PyArray_FLAGS(self) & NPY_ARRAY_OWNDATA) {
         PyArray_XDECREF(self);
-        size_t nbytes = PyArray_NBYTES(self);
-        /*
-         * Allocation will never be 0, see comment in ctors.c
-         * line 820
-         */
-        if (nbytes == 0) {
-            PyArray_Descr *dtype = PyArray_DESCR(self);
-            nbytes = dtype->elsize ? dtype->elsize : 1;
-        }
+        size_t nbytes = PyArray_NBYTES_ALLOCATED(self);
         PyObject *handler = PyArray_HANDLER(self);
         if (handler == NULL) {
             /* This can happen if someone arbitrarily sets NPY_ARRAY_OWNDATA */
diff --git a/numpy/core/src/multiarray/methods.c b/numpy/core/src/multiarray/methods.c
index b0b6f42f12ca..c31a8292ce32 100644
--- a/numpy/core/src/multiarray/methods.c
+++ b/numpy/core/src/multiarray/methods.c
@@ -1934,7 +1934,7 @@ array_setstate(PyArrayObject *self, PyObject *args)
     PyObject *rawdata = NULL;
     char *datastr;
     Py_ssize_t len;
-    npy_intp size, dimensions[NPY_MAXDIMS];
+    npy_intp dimensions[NPY_MAXDIMS];
     int nd;
     npy_intp nbytes;
     int overflowed;
@@ -1976,11 +1976,7 @@ array_setstate(PyArrayObject *self, PyObject *args)
      * since fa could be a 0-d or scalar, and then
      * PyDataMem_UserFREE will be confused
      */
-    size_t n_tofree = PyArray_NBYTES(self);
-    if (n_tofree == 0) {
-        PyArray_Descr *dtype = PyArray_DESCR(self);
-        n_tofree = dtype->elsize ? dtype->elsize : 1;
-    }
+    size_t n_tofree = PyArray_NBYTES_ALLOCATED(self);
     Py_XDECREF(PyArray_DESCR(self));
     fa->descr = typecode;
     Py_INCREF(typecode);
@@ -1988,17 +1984,39 @@ array_setstate(PyArrayObject *self, PyObject *args)
     if (nd < 0) {
         return NULL;
     }
-    size = PyArray_MultiplyList(dimensions, nd);
-    if (size < 0) {
-        /* More items than are addressable */
-        return PyErr_NoMemory();
+    /*
+     * We should do two things here:
+     * 1. Validate the input, that it is neither invalid, nor "too big"
+     *    ("too big" ignores dimensios of size 0).
+     * 2. Find `PyArray_NBYTES` of the result, as this is what we may need to
+     *    copy from the pickled data (may not match allocation currently if 0).
+     * Compare with `PyArray_NewFromDescr`, raise MemoryError for simplicity.
+     */
+    npy_bool empty = NPY_FALSE;
+    nbytes = 1;
+    for (int i = 0; i < nd; i++) {
+        if (dimensions[i] < 0) {
+            PyErr_SetString(PyExc_TypeError,
+                    "impossible dimension while unpickling array");
+            return NULL;
+        }
+        if (dimensions[i] == 0) {
+            empty = NPY_TRUE;
+        }
+        overflowed = npy_mul_with_overflow_intp(
+                &nbytes, nbytes, dimensions[i]);
+        if (overflowed) {
+            return PyErr_NoMemory();
+        }
     }
     overflowed = npy_mul_with_overflow_intp(
-        &nbytes, size, PyArray_DESCR(self)->elsize);
+            &nbytes, nbytes, PyArray_DESCR(self)->elsize);
     if (overflowed) {
-        /* More bytes than are addressable */
         return PyErr_NoMemory();
     }
+    if (empty) {
+        nbytes = 0;
+    }
 
     if (PyDataType_FLAGCHK(typecode, NPY_LIST_PICKLE)) {
         if (!PyList_Check(rawdata)) {
@@ -2039,8 +2057,7 @@ array_setstate(PyArrayObject *self, PyObject *args)
 
         if (len != nbytes) {
             PyErr_SetString(PyExc_ValueError,
-                            "buffer size does not"  \
-                            " match array size");
+                    "buffer size does not match array size");
             Py_DECREF(rawdata);
             return NULL;
         }
@@ -2097,21 +2114,18 @@ array_setstate(PyArrayObject *self, PyObject *args)
         /* Bytes should always be considered immutable, but we just grab the
          * pointer if they are large, to save memory. */
         if (!IsAligned(self) || swap || (len <= 1000)) {
-            npy_intp num = PyArray_NBYTES(self);
-            if (num == 0) {
-                Py_DECREF(rawdata);
-                Py_RETURN_NONE;
-            }
+            npy_intp num = PyArray_NBYTES_ALLOCATED(self);
             /* Store the handler in case the default is modified */
             Py_XDECREF(fa->mem_handler);
             fa->mem_handler = PyDataMem_GetHandler();
             if (fa->mem_handler == NULL) {
+                Py_CLEAR(fa->mem_handler);
                 Py_DECREF(rawdata);
                 return NULL;
             }
             fa->data = PyDataMem_UserNEW(num, PyArray_HANDLER(self));
             if (PyArray_DATA(self) == NULL) {
-                Py_DECREF(fa->mem_handler);
+                Py_CLEAR(fa->mem_handler);
                 Py_DECREF(rawdata);
                 return PyErr_NoMemory();
             }
@@ -2158,11 +2172,8 @@ array_setstate(PyArrayObject *self, PyObject *args)
         }
     }
     else {
-        npy_intp num = PyArray_NBYTES(self);
-        int elsize = PyArray_DESCR(self)->elsize;
-        if (num == 0 || elsize == 0) {
-            Py_RETURN_NONE;
-        }
+        npy_intp num = PyArray_NBYTES_ALLOCATED(self);
+
         /* Store the functions in case the default handler is modified */
         Py_XDECREF(fa->mem_handler);
         fa->mem_handler = PyDataMem_GetHandler();
@@ -2171,7 +2182,7 @@ array_setstate(PyArrayObject *self, PyObject *args)
         }
         fa->data = PyDataMem_UserNEW(num, PyArray_HANDLER(self));
         if (PyArray_DATA(self) == NULL) {
-            Py_DECREF(fa->mem_handler);
+            Py_CLEAR(fa->mem_handler);
             return PyErr_NoMemory();
         }
         if (PyDataType_FLAGCHK(PyArray_DESCR(self), NPY_NEEDS_INIT)) {
@@ -2180,7 +2191,6 @@ array_setstate(PyArrayObject *self, PyObject *args)
         PyArray_ENABLEFLAGS(self, NPY_ARRAY_OWNDATA);
         fa->base = NULL;
         if (_setlist_pkl(self, rawdata) < 0) {
-            Py_DECREF(fa->mem_handler);
             return NULL;
         }
     }