diff --git a/eliot/json.py b/eliot/json.py
index e83df9c..8eaa16c 100644
--- a/eliot/json.py
+++ b/eliot/json.py
@@ -88,7 +88,8 @@ def json_default(o: object) -> object:
         if isinstance(o, polars.Datetime):
             return o.isoformat()
 
-    raise TypeError("Unsupported type")
+    # Fall back to repr() get _some_ useful value to log
+    return repr(o)
 
 
 if platform.python_implementation() == "PyPy":
diff --git a/eliot/tests/test_json.py b/eliot/tests/test_json.py
index 76cabca..7961dea 100644
--- a/eliot/tests/test_json.py
+++ b/eliot/tests/test_json.py
@@ -73,8 +73,8 @@ def test_numpy_not_imported(self):
 
         This ensures NumPy isn't a hard dependency.
         """
-        with self.assertRaises(TypeError):
-            dumps([object()], default=json_default)
+        weird_val = object()
+        self.assertEqual(dumps([weird_val], default=json_default), dumps([repr(weird_val)]))
         self.assertEqual(dumps(12, default=json_default), "12")
 
     @skipUnless(np, "NumPy is not installed.")
@@ -206,3 +206,11 @@ class TestDataClass:
         obj = TestDataClass(name="test", value=42)
         serialized = loads(dumps(obj, default=json_default))
         self.assertEqual(serialized, {"name": "test", "value": 42})
+
+    def test_unserializable(self):
+        """Test that even values without dedicated JSON serialization
+        support dump without errors."""
+        def unserializable():
+            pass
+
+        self.assertEqual(dumps(unserializable, default=json_default), dumps(repr(unserializable)))