BUG: PeriodArray.__sub__(Period) overflows

doc/source/whatsnew/v1.5.0.rst

@@ -904,6 +904,7 @@ Period
 - Bug in constructing a :class:`Period` from a :class:`Timestamp` or ``np.datetime64`` object with non-zero nanoseconds and ``freq="ns"`` incorrectly truncating the nanoseconds (:issue:`46811`)
 - Bug in adding ``np.timedelta64("NaT", "ns")`` to a :class:`Period` with a timedelta-like freq incorrectly raising ``IncompatibleFrequency`` instead of returning ``NaT`` (:issue:`47196`)
 - Bug in adding an array of integers to an array with :class:`PeriodDtype` giving incorrect results when ``dtype.freq.n > 1`` (:issue:`47209`)
+- Bug in subtracting a :class:`Period` from an array with :class:`PeriodDtype` returning incorrect results instead of raising ``OverflowError`` when the operation overflows (:issue:`47538`)
 -
 
 Plotting

pandas/core/arrays/datetimelike.py

@@ -1182,8 +1182,9 @@ def _sub_period(self, other: Period) -> npt.NDArray[np.object_]:
         # If the operation is well-defined, we return an object-dtype ndarray
         # of DateOffsets.  Null entries are filled with pd.NaT
         self._check_compatible_with(other)
-        asi8 = self.asi8
-        new_i8_data = asi8 - other.ordinal  # TODO: checked_add_with_arr
+        new_i8_data = checked_add_with_arr(
+            self.asi8, -other.ordinal, arr_mask=self._isnan
+        )
         new_data = np.array([self.freq.base * x for x in new_i8_data])
 
         if self._hasna:

pandas/tests/arrays/test_period.py

@@ -115,6 +115,20 @@ def test_sub_period():
         arr - other
 
 
+def test_sub_period_overflow():
+    # GH#47538
+    dti = pd.date_range("1677-09-22", periods=2, freq="D")
+    pi = dti.to_period("ns")
+
+    per = pd.Period._from_ordinal(10**14, pi.freq)
+
+    with pytest.raises(OverflowError, match="Overflow in int64 addition"):
+        pi - per
+
+    with pytest.raises(OverflowError, match="Overflow in int64 addition"):
+        per - pi
+
+
 # ----------------------------------------------------------------------------
 # Methods