following up on comments from rhshadrach

Author: veljanin

doc/source/whatsnew/v3.0.0.rst

@@ -544,8 +544,7 @@ Bug fixes
 
 Categorical
 ^^^^^^^^^^^
--
--
+- Bug in :func:`convert_dtypes` with ``dtype_backend='pyarrow'`` parameter where empty categorical series raise error or get converted to null[pyarrow] (:issue:`59934`)
 
 Datetimelike
 ^^^^^^^^^^^^

pandas/core/dtypes/cast.py

@@ -1143,6 +1143,7 @@ def convert_dtypes(
                 base_dtype.kind == "O"  # type: ignore[union-attr]
                 and input_array.size > 0
                 and isna(input_array).all()
+                and not isinstance(input_array.dtype, CategoricalDtype)
             ):
                 import pyarrow as pa
 

pandas/tests/frame/methods/test_convert_dtypes.py

@@ -34,6 +34,26 @@ def test_convert_empty(self):
         # Empty DataFrame can pass convert_dtypes, see GH#40393
         empty_df = pd.DataFrame()
         tm.assert_frame_equal(empty_df, empty_df.convert_dtypes())
+    
+    def test_convert_empty_categorical_to_pyarrow(self):
+        # GH#59934
+        df = pd.DataFrame(
+            {
+                "A": pd.Categorical([None] * 5),
+                "B": pd.Categorical([None] * 5, categories=["B1", "B2"]),
+            }
+        )
+        converted = df.convert_dtypes(dtype_backend="pyarrow")
+        expected = df
+        tm.assert_frame_equal(converted, expected)
+
+        assert converted.A.dtype == "category", "Dtype in column A is not 'category'"
+        assert converted.B.dtype == "category", "Dtype in column B is not 'category'"
+        assert converted.A.cat.categories.empty, "Categories in column A are not empty"
+        assert (
+            converted.B.cat.categories.__contains__("B1")
+            and converted.B.cat.categories.__contains__("B2")
+        ), "Categories in column B doesn't contain adequate categories"
 
     def test_convert_dtypes_retain_column_names(self):
         # GH#41435

pandas/tests/series/methods/test_convert_dtypes.py

@@ -297,3 +297,20 @@ def test_convert_dtypes_pyarrow_null(self):
         result = ser.convert_dtypes(dtype_backend="pyarrow")
         expected = pd.Series([None, None], dtype=pd.ArrowDtype(pa.null()))
         tm.assert_series_equal(result, expected)
+
+    def test_convert_empty_categorical_to_pyarrow(self):
+        # GH#59934
+        ser1 = pd.Series(pd.Categorical([None] * 5))
+        converted1 = ser1.convert_dtypes(dtype_backend="pyarrow")
+        expected = ser1
+        
+        tm.assert_series_equal(converted1, expected)
+        assert converted1.dtype == "category", "Series dtype is not 'category'"
+        assert converted1.cat.categories.empty, "Series categories are not empty"
+
+        ser2 = pd.Series(pd.Categorical([None] * 5, categories=["S1", "S2"]))
+        converted2 = ser2.convert_dtypes(dtype_backend="pyarrow")
+        assert (
+            converted2.cat.categories.__contains__("S1")
+            and converted2.cat.categories.__contains__("S2")
+        ), "Categories in ser2 doesn't contain adequate categories"