diff --git a/numpy/core/src/multiarray/ctors.c b/numpy/core/src/multiarray/ctors.c
index 6e6f67e7d80b..851244adfa7d 100644
--- a/numpy/core/src/multiarray/ctors.c
+++ b/numpy/core/src/multiarray/ctors.c
@@ -741,7 +741,13 @@ discover_dimensions(PyObject *obj, int *maxndim, npy_intp *d, int check_it,
     if (!PySequence_Check(obj) ||
             PySequence_Length(obj) < 0) {
         *maxndim = 0;
-        PyErr_Clear();
+        if (PyErr_Occurred()) {
+            if (PyErr_ExceptionMatches(PyExc_RecursionError) ||
+                    PyErr_ExceptionMatches(PyExc_MemoryError)) {
+                return -1;
+            }
+            PyErr_Clear();
+        }
         return 0;
     }
 
@@ -780,7 +786,14 @@ discover_dimensions(PyObject *obj, int *maxndim, npy_intp *d, int check_it,
         return 0;
     }
     else if (PyErr_Occurred()) {
-        /* TODO[gh-14801]: propagate crashes during attribute access? */
+        /*
+         * Clear all but clearly fatal errors (previously cleared all).
+         * 1.20+ does not clear any errors here.
+         */
+        if (PyErr_ExceptionMatches(PyExc_RecursionError) ||
+                PyErr_ExceptionMatches(PyExc_MemoryError)) {
+            return -1;
+        }
         PyErr_Clear();
     }
 
@@ -1740,7 +1753,8 @@ PyArray_GetArrayParamsFromObject_int(PyObject *op,
         else {
             *out_dtype = NULL;
             if (PyArray_DTypeFromObject(op, NPY_MAXDIMS, out_dtype) < 0) {
-                if (PyErr_ExceptionMatches(PyExc_MemoryError)) {
+                if (PyErr_ExceptionMatches(PyExc_MemoryError) ||
+                        PyErr_ExceptionMatches(PyExc_RecursionError)) {
                     return -1;
                 }
                 /* Return NPY_OBJECT for most exceptions */
@@ -2404,7 +2418,14 @@ PyArray_FromInterface(PyObject *origin)
                                                     "__array_interface__");
     if (iface == NULL) {
         if (PyErr_Occurred()) {
-            PyErr_Clear(); /* TODO[gh-14801]: propagate crashes during attribute access? */
+            /*
+             * Clear all but clearly fatal errors (previously cleared all).
+             * 1.20+ does not clear any errors here.
+             */
+            if (PyErr_ExceptionMatches(PyExc_RecursionError) ||
+                    PyErr_ExceptionMatches(PyExc_MemoryError)) {
+                return NULL;
+            }
         }
         return Py_NotImplemented;
     }
@@ -2672,7 +2693,15 @@ PyArray_FromArrayAttr(PyObject *op, PyArray_Descr *typecode, PyObject *context)
     array_meth = PyArray_LookupSpecial_OnInstance(op, "__array__");
     if (array_meth == NULL) {
         if (PyErr_Occurred()) {
-            PyErr_Clear(); /* TODO[gh-14801]: propagate crashes during attribute access? */
+            /*
+             * Clear all but clearly fatal errors (previously cleared all).
+             * 1.20+ does not clear any errors here.
+             */
+            if (PyErr_ExceptionMatches(PyExc_RecursionError) ||
+                    PyErr_ExceptionMatches(PyExc_MemoryError)) {
+                return NULL;
+            }
+            PyErr_Clear();
         }
         return Py_NotImplemented;
     }
diff --git a/numpy/core/tests/test_multiarray.py b/numpy/core/tests/test_multiarray.py
index f7c7b0ad9eab..2d087f7ca2f2 100644
--- a/numpy/core/tests/test_multiarray.py
+++ b/numpy/core/tests/test_multiarray.py
@@ -818,6 +818,37 @@ def __array__(self, dtype=None):
 
         assert_raises(ValueError, np.array, x())
 
+    @pytest.mark.parametrize("error", [RecursionError, MemoryError])
+    @pytest.mark.parametrize("attribute",
+        ["__array_interface__", "__array__", "__array_struct__"])
+    def test_bad_array_like_attributes(self, attribute, error):
+        # Check that errors during attribute retrieval are raised unless
+        # they are Attribute errors.
+
+        class BadInterface:
+           def __getattr__(self, attr):
+               if attr == attribute:
+                   raise error
+               super().__getattr__(attr)
+
+        with pytest.raises(error):
+            np.array(BadInterface())
+
+    @pytest.mark.parametrize("error", [RecursionError, MemoryError])
+    def test_bad_array_like_bad_length(self, error):
+        # RecursionError and MemoryError are considered "critical" in
+        # sequences. We could expand this more generally though. (NumPy 1.20)
+        class BadSequence:
+            def __len__(self):
+                raise error
+            def __getitem__(self):
+                # must have getitem to be a Sequence
+                return 1
+
+        with pytest.raises(error):
+            np.array(BadSequence())
+
+
     def test_from_string(self):
         types = np.typecodes['AllInteger'] + np.typecodes['Float']
         nstr = ['123', '123']