diff --git a/pandas/core/indexes/period.py b/pandas/core/indexes/period.py
index b59c32bb8a9d4..5e4dd2998a3be 100644
--- a/pandas/core/indexes/period.py
+++ b/pandas/core/indexes/period.py
@@ -322,13 +322,9 @@ def _shallow_copy(self, values=None, **kwargs):
                 # this quite a bit.
                 values = period_array(values, freq=self.freq)
 
-        # I don't like overloading shallow_copy with freq changes.
-        # See if it's used anywhere outside of test_resample_empty_dataframe
+        # We don't allow changing `freq` in _shallow_copy.
+        validate_dtype_freq(self.dtype, kwargs.get('freq'))
         attributes = self._get_attributes_dict()
-        freq = kwargs.pop("freq", None)
-        if freq:
-            values = values.asfreq(freq)
-            attributes.pop("freq", None)
 
         attributes.update(kwargs)
         if not len(values) and 'dtype' not in kwargs:
diff --git a/pandas/core/resample.py b/pandas/core/resample.py
index ee9137c264edc..25604b29f22f6 100644
--- a/pandas/core/resample.py
+++ b/pandas/core/resample.py
@@ -404,7 +404,10 @@ def _wrap_result(self, result):
 
         if isinstance(result, ABCSeries) and result.empty:
             obj = self.obj
-            result.index = obj.index._shallow_copy(freq=to_offset(self.freq))
+            if isinstance(obj.index, PeriodIndex):
+                result.index = obj.index.asfreq(self.freq)
+            else:
+                result.index = obj.index._shallow_copy(freq=self.freq)
             result.name = getattr(obj, 'name', None)
 
         return result
diff --git a/pandas/tests/indexes/period/test_period.py b/pandas/tests/indexes/period/test_period.py
index 53f28612305c2..464ff7aa5d58d 100644
--- a/pandas/tests/indexes/period/test_period.py
+++ b/pandas/tests/indexes/period/test_period.py
@@ -1,6 +1,7 @@
 import numpy as np
 import pytest
 
+from pandas._libs.tslibs.period import IncompatibleFrequency
 import pandas.util._test_decorators as td
 
 import pandas as pd
@@ -40,9 +41,7 @@ def test_where(self):
     @pytest.mark.parametrize('use_numpy', [True, False])
     @pytest.mark.parametrize('index', [
         pd.period_range('2000-01-01', periods=3, freq='D'),
-        pytest.param(
-            pd.period_range('2001-01-01', periods=3, freq='2D'),
-            marks=pytest.mark.xfail(reason='GH 24391')),
+        pd.period_range('2001-01-01', periods=3, freq='2D'),
         pd.PeriodIndex(['2001-01', 'NaT', '2003-01'], freq='M')])
     def test_repeat_freqstr(self, index, use_numpy):
         # GH10183
@@ -117,6 +116,17 @@ def test_shallow_copy_empty(self):
 
         tm.assert_index_equal(result, expected)
 
+    def test_shallow_copy_i8(self):
+        # GH-24391
+        pi = period_range("2018-01-01", periods=3, freq="2D")
+        result = pi._shallow_copy(pi.asi8, freq=pi.freq)
+        tm.assert_index_equal(result, pi)
+
+    def test_shallow_copy_changing_freq_raises(self):
+        pi = period_range("2018-01-01", periods=3, freq="2D")
+        with pytest.raises(IncompatibleFrequency, match="are different"):
+            pi._shallow_copy(pi, freq="H")
+
     def test_dtype_str(self):
         pi = pd.PeriodIndex([], freq='M')
         assert pi.dtype_str == 'period[M]'
diff --git a/pandas/tests/resample/test_base.py b/pandas/tests/resample/test_base.py
index 0efd48c25ad62..911cd990ab881 100644
--- a/pandas/tests/resample/test_base.py
+++ b/pandas/tests/resample/test_base.py
@@ -109,7 +109,10 @@ def test_resample_empty_series_all_ts(freq, empty_series, resample_method):
     result = getattr(s.resample(freq), resample_method)()
 
     expected = s.copy()
-    expected.index = s.index._shallow_copy(freq=freq)
+    if isinstance(s.index, PeriodIndex):
+        expected.index = s.index.asfreq(freq=freq)
+    else:
+        expected.index = s.index._shallow_copy(freq=freq)
     assert_index_equal(result.index, expected.index)
     assert result.index.freq == expected.index.freq
     assert_series_equal(result, expected, check_dtype=False)
@@ -127,7 +130,10 @@ def test_resample_empty_dataframe_all_ts(empty_frame, freq, resample_method):
         # GH14962
         expected = Series([])
 
-    expected.index = df.index._shallow_copy(freq=freq)
+    if isinstance(df.index, PeriodIndex):
+        expected.index = df.index.asfreq(freq=freq)
+    else:
+        expected.index = df.index._shallow_copy(freq=freq)
     assert_index_equal(result.index, expected.index)
     assert result.index.freq == expected.index.freq
     assert_almost_equal(result, expected, check_dtype=False)