BUG: incorrect freq in PeriodIndex-Period (#33801)

Author: jbrockmendel

pandas/core/indexes/datetimelike.py

@@ -88,7 +88,7 @@ def wrapped(self, other):
         if result is NotImplemented:
             return NotImplemented
 
-        new_freq = self._get_addsub_freq(other)
+        new_freq = self._get_addsub_freq(other, result)
         result._freq = new_freq
         return result
 
@@ -451,14 +451,16 @@ def _partial_date_slice(
     # --------------------------------------------------------------------
     # Arithmetic Methods
 
-    def _get_addsub_freq(self, other) -> Optional[DateOffset]:
+    def _get_addsub_freq(self, other, result) -> Optional[DateOffset]:
         """
         Find the freq we expect the result of an addition/subtraction operation
         to have.
         """
         if is_period_dtype(self.dtype):
-            # Only used for ops that stay PeriodDtype
-            return self.freq
+            if is_period_dtype(result.dtype):
+                # Only used for ops that stay PeriodDtype
+                return self.freq
+            return None
         elif self.freq is None:
             return None
         elif lib.is_scalar(other) and isna(other):

pandas/tests/arithmetic/test_period.py

@@ -1444,8 +1444,13 @@ def test_pi_sub_period(self):
         tm.assert_index_equal(result, exp)
 
         exp = pd.TimedeltaIndex([np.nan, np.nan, np.nan, np.nan], name="idx")
-        tm.assert_index_equal(idx - pd.Period("NaT", freq="M"), exp)
-        tm.assert_index_equal(pd.Period("NaT", freq="M") - idx, exp)
+        result = idx - pd.Period("NaT", freq="M")
+        tm.assert_index_equal(result, exp)
+        assert result.freq == exp.freq
+
+        result = pd.Period("NaT", freq="M") - idx
+        tm.assert_index_equal(result, exp)
+        assert result.freq == exp.freq
 
     def test_pi_sub_pdnat(self):
         # GH#13071