BUG: fix PeriodIndex.difference producing incorrect results

doc/source/whatsnew/v3.0.0.rst

@@ -691,6 +691,7 @@ Indexing
 - Bug in :meth:`DataFrame.__getitem__` returning modified columns when called with ``slice`` in Python 3.12 (:issue:`57500`)
 - Bug in :meth:`DataFrame.from_records` throwing a ``ValueError`` when passed an empty list in ``index`` (:issue:`58594`)
 - Bug in :meth:`MultiIndex.insert` when a new value inserted to a datetime-like level gets cast to ``NaT`` and fails indexing (:issue:`60388`)
+- Bug in :meth:`PeriodIndex.difference` producing incorrect results when operating between :class:`PeriodIndex` and :class:`Index` objects (:issue:`58971`)
 - Bug in printing :attr:`Index.names` and :attr:`MultiIndex.levels` would not escape single quotes (:issue:`60190`)
 
 Missing

pandas/core/indexes/period.py

@@ -534,6 +534,22 @@ def shift(self, periods: int = 1, freq=None) -> Self:
             )
         return self + periods
 
+    def _convert_can_do_setop(self, other):
+        try:
+            if isinstance(other, Index):
+                # Handle empty cases
+                if other.empty:
+                    return super()._convert_can_do_setop(other)
+
+                # Convert non-PeriodIndex to PeriodIndex
+                if not isinstance(other, PeriodIndex):
+                    other = PeriodIndex(other, freq=self.freq)
+
+        except (TypeError, ValueError):
+            return super()._convert_can_do_setop(other)
+
+        return super()._convert_can_do_setop(other)
+
 
 def period_range(
     start=None,

pandas/tests/indexes/period/test_setops.py

@@ -361,3 +361,16 @@ def test_union_duplicates(self):
             freq="D",
         )
         tm.assert_index_equal(result, expected)
+
+    def test_difference_periodindex_with_index(self):
+        # GH#58971
+        index1 = period_range("2022-01", periods=5, freq="M")
+        index2 = pd.Index(["2022-02", "2022-03"])
+
+        result1 = index1.difference(index2)
+        expected1 = PeriodIndex(["2022-01", "2022-04", "2022-05"], freq="M")
+        tm.assert_index_equal(result1, expected1)
+
+        result2 = index2.difference(index1)
+        expected2 = pd.Index([])
+        tm.assert_index_equal(result2, expected2)