diff --git a/src/journal/fuzz-journald-stream.c b/src/journal/fuzz-journald-stream.c
index 3ad9e20222..f9c6bfba10 100644
--- a/src/journal/fuzz-journald-stream.c
+++ b/src/journal/fuzz-journald-stream.c
@@ -32,7 +32,7 @@ int LLVMFuzzerTestOneInput(const uint8_t *data, size_t size) {
                 sd_event_run(s->event, UINT64_MAX);
 
         if (s->n_stdout_streams > 0)
-                stdout_stream_destroy(stream);
+                stdout_stream_terminate(stream);
 
         return 0;
 }
diff --git a/src/journal/journald-server.c b/src/journal/journald-server.c
index 6144ff0de0..a33c4b2824 100644
--- a/src/journal/journald-server.c
+++ b/src/journal/journald-server.c
@@ -2270,7 +2270,8 @@ int server_start_or_stop_idle_timer(Server *s) {
 
         assert(s);
 
-        if (!server_is_idle(s)) {
+        if (sd_event_get_state(s->event) == SD_EVENT_FINISHED ||
+            !server_is_idle(s)) {
                 s->idle_event_source = sd_event_source_disable_unref(s->idle_event_source);
                 return 0;
         }
diff --git a/src/journal/journald-stream.c b/src/journal/journald-stream.c
index 2ada374b73..e45765df0c 100644
--- a/src/journal/journald-stream.c
+++ b/src/journal/journald-stream.c
@@ -137,7 +137,7 @@ StdoutStream* stdout_stream_free(StdoutStream *s) {
 
 DEFINE_TRIVIAL_CLEANUP_FUNC(StdoutStream*, stdout_stream_free);
 
-void stdout_stream_destroy(StdoutStream *s) {
+void stdout_stream_terminate(StdoutStream *s) {
         if (!s)
                 return;
 
@@ -649,7 +649,7 @@ static int stdout_stream_process(sd_event_source *es, int fd, uint32_t revents,
         return 1;
 
 terminate:
-        stdout_stream_destroy(s);
+        stdout_stream_terminate(s);
         return 0;
 }
 
diff --git a/src/journal/journald-stream.h b/src/journal/journald-stream.h
index 7b756c05ec..71d3394ed9 100644
--- a/src/journal/journald-stream.h
+++ b/src/journal/journald-stream.h
@@ -11,5 +11,5 @@ int server_restore_streams(Server *s, FDSet *fds);
 
 StdoutStream* stdout_stream_free(StdoutStream *s);
 int stdout_stream_install(Server *s, int fd, StdoutStream **ret);
-void stdout_stream_destroy(StdoutStream *s);
+void stdout_stream_terminate(StdoutStream *s);
 void stdout_stream_send_notify(StdoutStream *s);