python
@@ -2644,6 +2644,29 @@ def test_pyimport_addmodule_create(self):
         mod = _testcapi.check_pyimport_addmodule(name)
         self.assertIs(mod, sys.modules[name])
 
+    def test_pyimport_addmodule_borrowed_ref(self):
+        # gh-105922: Test PyImport_AddModule() with a custom sys.modules which
+        # doesn't keep a strong reference to the newly created module
+        import _testcapi
+        module_name = 'dontexist'
+
+        self.assertNotIn(module_name, sys.modules)
+        self.addCleanup(unload, module_name)
+
+        class CustomModules(dict):
+            def __setitem__(self, key, value):
+                if key == module_name:
+                    value = "REPLACE_VALUE"
+                super().__setitem__(key, value)
+
+        custom_modules = CustomModules()
+        with swap_attr(sys, 'modules', custom_modules):
+            _testcapi.pyimport_addmodule(module_name)
+
+        if module_name in sys.modules:
+            print("sys.modules CANNOT be overriden: "
+                  "{module_name} is in sys.modules")
+
 
 if __name__ == '__main__':
     # Test needs to be a package, so we can do relative imports.

diff --git a/Modules/_testcapimodule.c b/Modules/_testcapimodule.c
@@ -3372,6 +3372,26 @@ check_pyimport_addmodule(PyObject *self, PyObject *args)
 }
 
 
+static PyObject *
+test_pyimport_addmodule(PyObject *self, PyObject *args)
+{
+    const char *name;
+    if (!PyArg_ParseTuple(args, "s", &name)) {
+        return NULL;
+    }
+    PyObject *mod = PyImport_AddModule(name);
+    if (mod == NULL) {
+        if (!PyErr_Occurred()) {
+            PyErr_SetString(PyExc_AssertionError,
+                            "PyImport_AddModule returns NULL "
+                            "without setting an exception");
+        }
+        return NULL;
+    }
+    return Py_NewRef(mod);
+}
+
+
 static PyObject *
 test_weakref_capi(PyObject *Py_UNUSED(module), PyObject *Py_UNUSED(args))
 {
@@ -3610,6 +3630,7 @@ static PyMethodDef TestMethods[] = {
     {"function_set_kw_defaults", function_set_kw_defaults, METH_VARARGS, NULL},
     {"test_atexit", test_atexit, METH_NOARGS},
     {"check_pyimport_addmodule", check_pyimport_addmodule, METH_VARARGS},
+    {"pyimport_addmodule", test_pyimport_addmodule, METH_VARARGS},
     {"test_weakref_capi", test_weakref_capi, METH_NOARGS},
     {NULL, NULL} /* sentinel */
 };

@@ -373,16 +373,20 @@ PyImport_AddModuleObject(PyObject *name)
         return NULL;
     }
 
-    // gh-86160: PyImport_AddModuleObject() returns a borrowed reference
-    PyObject *ref = PyWeakref_NewRef(mod, NULL);
+    // Convert to a borrowed reference
-    // Convert to a borrowed reference
+    // Convert to a borrowed reference.
-    // Convert to a borrowed reference
+    // Convert to a borrowed reference.
+    Py_ssize_t old_refcnt = Py_REFCNT(mod);
     Py_DECREF(mod);
-    if (ref == NULL) {
+    if (old_refcnt == 1) {
+        // gh-86160, gh-105922: The module got deleted. It can happen if
+        // sys.modules does not hold a strong reference to the module. For
+        // example, if sys.modules is not a regular dict but a custom type.
+        PyErr_SetString(PyExc_RuntimeError,
+                        "sys.modules does not hold a strong reference "
+                        "to the module");
         return NULL;
     }
 
-    mod = PyWeakref_GetObject(ref);
-    Py_DECREF(ref);
-    return mod; /* borrowed reference */
+    return mod;  // borrowed reference, sys.modules holds a strong reference
 }