diff --git a/sh.py b/sh.py
index 84ed294d..14ad13a0 100644
--- a/sh.py
+++ b/sh.py
@@ -2306,7 +2306,11 @@ def __init__(
 
             def timeout_fn():
                 self.timed_out = True
-                self.signal(ca["timeout_signal"])
+                try:
+                    self.signal(ca["timeout_signal"])
+                except ProcessLookupError:
+                    # Edge case: the process probably exited
+                    pass
 
             self._timeout_event = None
             self._timeout_timer = None
diff --git a/tests/sh_test.py b/tests/sh_test.py
index 74e514e3..c3d19adf 100644
--- a/tests/sh_test.py
+++ b/tests/sh_test.py
@@ -3012,6 +3012,25 @@ def test_custom_timeout_signal(self):
         else:
             self.fail("we should have handled a TimeoutException")
 
+    def test_timeout_race_condition_process_exit(self):
+        import signal
+
+        from sh import TimeoutException
+
+        py = create_tmp_test(
+            """
+import time
+time.sleep(0.05)
+"""
+        )
+        # Run multiple times to increase likelihood of hitting the race condition
+        for _ in range(50):
+            try:
+                python(py.name, _timeout=0.1, _timeout_signal=signal.SIGTERM)
+            except TimeoutException:
+                # TimeoutException is OK, but ProcessLookupError isn't
+                pass
+
     def test_append_stdout(self):
         py = create_tmp_test(
             """