diff --git a/hive-priv/src/container.rs b/hive-priv/src/container.rs
index 7c0bb74e..c25bbdf1 100644
--- a/hive-priv/src/container.rs
+++ b/hive-priv/src/container.rs
@@ -728,18 +728,31 @@ mod tests {
         );
     }
 
-    /// Whether `pid` is gone, or only a zombie awaiting its reaper: either
-    /// way it is no longer running.
+    /// Whether `pid` is gone, a zombie (`Z`), or being reaped (`X`): none of
+    /// these runs again, and a process passes through them in that order,
+    /// so once this is true it stays true.
     fn is_dead(pid: &str) -> bool {
         match std::fs::read_to_string(format!("/proc/{pid}/stat")) {
             Err(_) => true,
-            // The state letter follows the parenthesised command name.
-            Ok(stat) => stat
-                .rsplit_once(") ")
-                .is_some_and(|(_, rest)| rest.starts_with('Z')),
+            Ok(stat) => stat_is_dead(&stat),
         }
     }
 
+    /// The state letter of a `/proc/<pid>/stat` line, which follows the
+    /// parenthesised command name, is `Z` or `X`.
+    fn stat_is_dead(stat: &str) -> bool {
+        stat.rsplit_once(") ")
+            .is_some_and(|(_, rest)| rest.starts_with(['Z', 'X']))
+    }
+
+    #[test]
+    fn zombie_and_reaped_states_count_as_dead() {
+        assert!(stat_is_dead("42 (sleep) Z 1 42 42"));
+        assert!(stat_is_dead("42 (sleep) X 1 42 42"));
+        assert!(!stat_is_dead("42 (sleep) S 1 42 42"));
+        assert!(!stat_is_dead("42 (sleep) R 1 42 42"));
+    }
+
     /// A child still running at the limit comes back `TimedOut`, and the kill
     /// reaches its whole process group: the backgrounded grandchild dies too,
     /// not just the shell that started it.