BUG: mask/where raising for mixed dtype frame and no other

pandas/core/generic.py

@@ -6123,8 +6123,8 @@ def _is_mixed_type(self) -> bool_t:
     def _check_inplace_setting(self, value) -> bool_t:
         """check whether we allow in-place setting with this type of value"""
         if self._is_mixed_type and not self._mgr.is_numeric_mixed_type:
-            # allow an actual np.nan thru
-            if is_float(value) and np.isnan(value):
+            # allow an actual np.nan through
+            if is_float(value) and np.isnan(value) or value is lib.no_default:
                 return True
 
             raise TypeError(

pandas/tests/frame/indexing/test_mask.py

@@ -141,3 +141,12 @@ def test_mask_return_dtype():
     excepted = Series([1.0, 0.0, 1.0, 0.0], dtype=ser.dtype)
     result = ser.mask(cond, other)
     tm.assert_series_equal(result, excepted)
+
+
+def test_mask_inplace_no_other():
+    # GH#51685
+    df = DataFrame({"a": [1, 2], "b": ["x", "y"]})
+    cond = DataFrame({"a": [True, False], "b": [False, True]})
+    df.mask(cond, inplace=True)
+    expected = DataFrame({"a": [np.nan, 2], "b": ["x", np.nan]})
+    tm.assert_frame_equal(df, expected)

pandas/tests/frame/indexing/test_where.py

@@ -1025,3 +1025,12 @@ def test_where_int_overflow(replacement):
     expected = DataFrame([[1.0, 2e25, "nine"], [replacement, 0.1, replacement]])
 
     tm.assert_frame_equal(result, expected)
+
+
+def test_where_inplace_no_other():
+    # GH#51685
+    df = DataFrame({"a": [1, 2], "b": ["x", "y"]})
+    cond = DataFrame({"a": [True, False], "b": [False, True]})
+    df.where(cond, inplace=True)
+    expected = DataFrame({"a": [1, np.nan], "b": [np.nan, "y"]})
+    tm.assert_frame_equal(df, expected)