diff --git a/host-setup/agent-safety/claude/install.py b/host-setup/agent-safety/claude/install.py
index 1d8a678d9..514388537 100755
--- a/host-setup/agent-safety/claude/install.py
+++ b/host-setup/agent-safety/claude/install.py
@@ -127,6 +127,18 @@ def matcher_sees_bash(matcher):
         return False
 
 
+def matcher_covers_every_exit_reason(matcher):
+    """Whether a SessionEnd matcher's shape runs on every exit reason rather than naming specific ones.
+
+    A SessionEnd matcher filters by exit reason the way a PreToolUse matcher filters by tool: an
+    absent or empty matcher runs on every reason and `*` is the all-reasons spelling, so none of
+    the three is a defect. Unlike `matcher_sees_bash`, there is no single reason to test regex
+    membership against, since the sweep must fire on every exit reason rather than one particular
+    one, so this classifies the shape rather than evaluating a pattern.
+    """
+    return matcher is None or matcher in ("", "*")
+
+
 def owns(entry, prefix):
     """Whether an allow rule names the script the prefix identifies, rather than a longer path.
 
@@ -510,12 +522,12 @@ def event_groups(event):
                 )
                 continue
             swept += 1
-            # A SessionEnd matcher filters by exit reason, so a sweep under one runs on that reason alone.
+            # A matcher naming specific exit reasons runs the sweep on those reasons alone.
             # Counting it as registered reports a machine current while the sweep never fires on an ordinary exit.
-            if "matcher" in group:
+            if not matcher_covers_every_exit_reason(group.get("matcher")):
                 report(
                     f"the SessionEnd sweep is registered under a matcher "
-                    f"({group['matcher']!r}), so it runs on that exit reason alone"
+                    f"({group.get('matcher')!r}), so it runs on that exit reason alone"
                 )
     if ends is None:
         pass  # likewise reported as a shape error above
@@ -811,13 +823,13 @@ def reject(where, held, want):
     done = ["PreToolUse/Bash hook registered"]
 
     # Step 2b registers the SessionEnd sweep the same strip-then-register way as the guard above.
-    # The group carries no matcher, so it fires on every exit reason rather than on one.
+    # The chosen or newly created group covers every exit reason, so the sweep fires on all of them.
     ends = data.setdefault("hooks", {}).setdefault("SessionEnd", [])
     for g in ends:
         hooks_list = g.get("hooks")
         if isinstance(hooks_list, list):
             hooks_list[:] = [h for h in hooks_list if SWEEP_STEM not in str(h.get("command", ""))]
-    end_group = next((g for g in ends if "matcher" not in g), None)
+    end_group = next((g for g in ends if matcher_covers_every_exit_reason(g.get("matcher"))), None)
     if end_group is None:
         end_group = {"hooks": []}
         ends.append(end_group)
diff --git a/host-setup/agent-safety/claude/test_install.py b/host-setup/agent-safety/claude/test_install.py
index d9c73a866..9ad938ff0 100755
--- a/host-setup/agent-safety/claude/test_install.py
+++ b/host-setup/agent-safety/claude/test_install.py
@@ -389,6 +389,25 @@ def test_reinstalling_does_not_duplicate_the_sweep(self):
         ]
         self.assertEqual(len(entries), 1)
 
+    def test_reinstalling_reuses_a_sweep_group_covering_every_reason(self):
+        """`*` and `""` cover every reason the same as absent, so reinstalling must reuse that group
+        rather than read only the matcherless shape and leave a second, empty one behind."""
+        self.install()
+        for matcher in ("*", ""):
+            with self.subTest(matcher=matcher):
+                data = self._settings()
+                data["hooks"]["SessionEnd"][0]["matcher"] = matcher
+                self._write(data)
+                self.install()
+                groups = self._settings()["hooks"]["SessionEnd"]
+                owning = [
+                    g
+                    for g in groups
+                    if any(install.SWEEP_STEM in h.get("command", "") for h in g.get("hooks", []))
+                ]
+                self.assertEqual(len(owning), 1, groups)
+                self.assertEqual(owning[0].get("matcher"), matcher)
+
     def test_a_wrong_hooks_shape_is_reported_as_itself(self):
         """Iterating a dict yields keys and a string yields characters, so a wrong shape read as
         zero registrations and sent a reader to the wrong fix."""
@@ -572,6 +591,22 @@ def test_a_sweep_under_a_matcher_reports_stale(self):
         self.assertEqual(r.returncode, 1, r.stdout + r.stderr)
         self.assertIn("under a matcher", r.stdout)
 
+    def test_a_sweep_matcher_covering_every_reason_is_not_a_defect(self):
+        """An absent, empty, or `*` SessionEnd matcher runs on every exit reason, same as PreToolUse."""
+        self.install()
+        for matcher in ("*", ""):
+            with self.subTest(matcher=matcher):
+                data = self._settings()
+                data["hooks"]["SessionEnd"][0]["matcher"] = matcher
+                self._write(data)
+                problems = install.registration_problems(self.home)
+                self.assertEqual([p for p in problems if "under a matcher" in p], [], matcher)
+        data = self._settings()
+        data["hooks"]["SessionEnd"][0].pop("matcher", None)
+        self._write(data)
+        problems = install.registration_problems(self.home)
+        self.assertEqual([p for p in problems if "under a matcher" in p], [])
+
     def test_an_unregistered_sweep_reports_stale_rather_than_current(self):
         self.install()
         data = self._settings()