diff --git a/coverage/data.py b/coverage/data.py
index b209cf157..4bdfe3010 100644
--- a/coverage/data.py
+++ b/coverage/data.py
@@ -70,7 +70,7 @@ def combinable_files(data_file, data_paths=None):
         if os.path.isfile(p):
             files_to_combine.append(os.path.abspath(p))
         elif os.path.isdir(p):
-            pattern = os.path.join(os.path.abspath(p), f"{local}.*")
+            pattern = glob.escape(os.path.join(os.path.abspath(p), local)) +".*"
             files_to_combine.extend(glob.glob(pattern))
         else:
             raise NoDataError(f"Couldn't combine from non-existent path '{p}'")
diff --git a/coverage/sqldata.py b/coverage/sqldata.py
index 8d2ed73a5..564d4ec93 100644
--- a/coverage/sqldata.py
+++ b/coverage/sqldata.py
@@ -774,8 +774,8 @@ def erase(self, parallel=False):
         file_be_gone(self._filename)
         if parallel:
             data_dir, local = os.path.split(self._filename)
-            localdot = local + ".*"
-            pattern = os.path.join(os.path.abspath(data_dir), localdot)
+            local_abs_path = os.path.join(os.path.abspath(data_dir), local)
+            pattern = glob.escape(local_abs_path) + ".*"
             for filename in glob.glob(pattern):
                 if self._debug.should("dataio"):
                     self._debug.write(f"Erasing parallel data file {filename!r}")