diff --git a/Lib/inspect.py b/Lib/inspect.py
--- a/Lib/inspect.py
+++ b/Lib/inspect.py
@@ -1975,6 +1975,28 @@
         parameters = []
         empty = Parameter.empty
 
+        def parse_name(node):
+            id = node.id
+            ctx = node.ctx
+            if (not isinstance(ctx, ast.Load)) or (id not in sys.modules):
+                return None
+            return sys.modules[id]
+
+        def parse_attribute(node):
+            if not isinstance(node.ctx, ast.Load):
+                return None
+            value = node.value
+            attr = node.attr
+            if isinstance(value, ast.Attribute):
+                o = parse_attribute(value)
+            elif isinstance(value, ast.Name):
+                o = parse_name(value)
+            else:
+                return None
+            if not (o and hasattr(o, attr)):
+                return None
+            return getattr(o, attr)
+
         def p(name_node, default_node, default=empty):
             name = name_node.arg
 
@@ -1982,6 +2004,8 @@
                 default = default.n
             elif isinstance(default_node, ast.NameConstant):
                 default = default_node.value
+            elif isinstance(default_node, ast.Attribute):
+                default = parse_attribute(default_node)
             parameters.append(Parameter(name, kind, default=default, annotation=empty))
 
         # non-keyword-only parameters
diff --git a/Modules/posixmodule.c b/Modules/posixmodule.c
--- a/Modules/posixmodule.c
+++ b/Modules/posixmodule.c
@@ -2430,7 +2430,7 @@
 [clinic]*/
 
 PyDoc_STRVAR(os_stat__doc__,
-"stat(path, *, dir_fd=None, follow_symlinks=True)\n"
+"stat(path, *, dir_fd=None, follow_symlinks=True, fake=sys.maxsize)\n"
 "Perform a stat system call on the given path.\n"
 "\n"
 "  path\n"
diff --git a/x.py b/x.py
new file mode 100644
--- /dev/null
+++ b/x.py
@@ -0,0 +1,12 @@
+import ast
+import os
+import inspect
+
+fn = os.stat
+
+try:
+	print(inspect.signature(fn))
+except Exception as e:
+	print(e)
+
+# print(ast.dump(ast.parse("def foo" + fn.__text_signature__ + ": pass")))