BUG: wide_to_long fails when stubname misses and i contains string type column

doc/source/whatsnew/v1.5.0.rst

@@ -1019,6 +1019,7 @@ Reshaping
 - Bug in :meth:`DataFrame.join` with a list when using suffixes to join DataFrames with duplicate column names (:issue:`46396`)
 - Bug in :meth:`DataFrame.pivot_table` with ``sort=False`` results in sorted index (:issue:`17041`)
 - Bug in :meth:`concat` when ``axis=1`` and ``sort=False`` where the resulting Index was a :class:`Int64Index` instead of a :class:`RangeIndex` (:issue:`46675`)
+- Bug in :meth:`wide_to_long` raises when ``stubnames`` is missing in columns and ``i`` contains string dtype column (:issue:`46044`)
 
 Sparse
 ^^^^^^

pandas/core/reshape/melt.py

@@ -131,7 +131,11 @@ def melt(
     for col in id_vars:
         id_data = frame.pop(col)
         if is_extension_array_dtype(id_data):
-            id_data = concat([id_data] * K, ignore_index=True)
+            if K > 0:
+                id_data = concat([id_data] * K, ignore_index=True)
+            else:
+                # We can't concat empty list. (GH 46044)
+                id_data = type(id_data)([], name=id_data.name, dtype=id_data.dtype)
         else:
             # error: Incompatible types in assignment (expression has type
             # "ndarray[Any, dtype[Any]]", variable has type "Series")

pandas/tests/reshape/test_melt.py

@@ -1086,3 +1086,27 @@ def test_warn_of_column_name_value(self):
         with tm.assert_produces_warning(FutureWarning):
             result = df.melt(id_vars="value")
             tm.assert_frame_equal(result, expected)
+
+    @pytest.mark.parametrize("dtype", ["O", "string"])
+    def test_missing_stubname(self, dtype):
+        # GH46044
+        df = DataFrame({"id": ["1", "2"], "a-1": [100, 200], "a-2": [300, 400]})
+        df = df.astype({"id": dtype})
+        result = wide_to_long(
+            df,
+            stubnames=["a", "b"],
+            i="id",
+            j="num",
+            sep="-",
+        )
+        index = pd.Index(
+            [("1", 1), ("2", 1), ("1", 2), ("2", 2)],
+            name=("id", "num"),
+        )
+        expected = DataFrame(
+            {"a": [100, 200, 300, 400], "b": [np.nan] * 4},
+            index=index,
+        )
+        new_level = expected.index.levels[0].astype(dtype)
+        expected.index = expected.index.set_levels(new_level, level=0)
+        tm.assert_frame_equal(result, expected)