diff --git a/Include/objimpl.h b/Include/objimpl.h
--- a/Include/objimpl.h
+++ b/Include/objimpl.h
@@ -232,6 +232,10 @@ PyAPI_FUNC(PyVarObject *) _PyObject_NewV
 /* C equivalent of gc.collect(). */
 PyAPI_FUNC(Py_ssize_t) PyGC_Collect(void);
 
+#ifndef Py_LIMITED_API
+PyAPI_FUNC(Py_ssize_t) _PyGC_CollectHard(void);
+#endif
+
 /* Test if a type has a GC head */
 #define PyType_IS_GC(t) PyType_HasFeature((t), Py_TPFLAGS_HAVE_GC)
 
diff --git a/Modules/gcmodule.c b/Modules/gcmodule.c
--- a/Modules/gcmodule.c
+++ b/Modules/gcmodule.c
@@ -850,7 +850,8 @@ get_time(void)
 /* This is the main function.  Read this to understand how the
  * collection process works. */
 static Py_ssize_t
-collect(int generation, Py_ssize_t *n_collected, Py_ssize_t *n_uncollectable)
+collect(int generation, Py_ssize_t *n_collected, Py_ssize_t *n_uncollectable,
+        int hard)
 {
     int i;
     Py_ssize_t m = 0; /* # objects collected */
@@ -997,10 +998,14 @@ collect(int generation, Py_ssize_t *n_co
     }
 
     if (PyErr_Occurred()) {
-        if (gc_str == NULL)
-            gc_str = PyUnicode_FromString("garbage collection");
-        PyErr_WriteUnraisable(gc_str);
-        Py_FatalError("unexpected exception during garbage collection");
+        if (hard)
+            PyErr_Clear();
+        else {
+            if (gc_str == NULL)
+                gc_str = PyUnicode_FromString("garbage collection");
+            PyErr_WriteUnraisable(gc_str);
+            Py_FatalError("unexpected exception during garbage collection");
+        }
     }
 
     /* Update stats */
@@ -1059,7 +1064,7 @@ collect_with_callback(int generation)
 {
     Py_ssize_t result, collected, uncollectable;
     invoke_gc_callback("start", generation, 0, 0);
-    result = collect(generation, &collected, &uncollectable);
+    result = collect(generation, &collected, &uncollectable, 0);
     invoke_gc_callback("stop", generation, collected, uncollectable);
     return result;
 }
@@ -1541,6 +1546,22 @@ PyGC_Collect(void)
     return n;
 }
 
+Py_ssize_t
+_PyGC_CollectHard(void)
+{
+    Py_ssize_t n;
+
+    if (collecting)
+        n = 0; /* already collecting, don't do anything */
+    else {
+        Py_ssize_t collected, uncollectable;
+        collecting = 1;
+        n = collect(NUM_GENERATIONS - 1, NULL, NULL, 1);
+        collecting = 0;
+    }
+
+    return n;
+}
 
 void
 _PyGC_DumpShutdownStats(void)
diff --git a/Python/import.c b/Python/import.c
--- a/Python/import.c
+++ b/Python/import.c
@@ -444,6 +444,7 @@ PyImport_Cleanup(void)
 
     /* Finally, clear and delete the modules directory */
     PyDict_Clear(modules);
+    _PyGC_CollectHard();
     interp->modules = NULL;
     Py_DECREF(modules);
 }