diff --git a/homeassistant/components/logbook/websocket_api.py b/homeassistant/components/logbook/websocket_api.py
index 82b1db1081c..1af44440803 100644
--- a/homeassistant/components/logbook/websocket_api.py
+++ b/homeassistant/components/logbook/websocket_api.py
@@ -356,7 +356,7 @@ async def ws_event_stream(
     )
 
     await _async_wait_for_recorder_sync(hass)
-    if not subscriptions:
+    if msg_id not in connection.subscriptions:
         # Unsubscribe happened while waiting for recorder
         return
 
@@ -388,6 +388,8 @@ async def ws_event_stream(
 
     if not subscriptions:
         # Unsubscribe happened while waiting for formatted events
+        # or there are no supported entities (all UOM or state class)
+        # or devices
         return
 
     live_stream.task = asyncio.create_task(
diff --git a/tests/components/logbook/test_websocket_api.py b/tests/components/logbook/test_websocket_api.py
index 291c487b35b..2dd08ec44ce 100644
--- a/tests/components/logbook/test_websocket_api.py
+++ b/tests/components/logbook/test_websocket_api.py
@@ -2089,3 +2089,52 @@ async def test_recorder_is_far_behind(hass, recorder_mock, hass_ws_client, caplo
     assert msg["success"]
 
     assert "Recorder is behind" in caplog.text
+
+
+@patch("homeassistant.components.logbook.websocket_api.EVENT_COALESCE_TIME", 0)
+async def test_subscribe_all_entities_have_uom(hass, recorder_mock, hass_ws_client):
+    """Test subscribe/unsubscribe logbook stream with entities that are always filtered."""
+    now = dt_util.utcnow()
+    await asyncio.gather(
+        *[
+            async_setup_component(hass, comp, {})
+            for comp in ("homeassistant", "logbook", "automation", "script")
+        ]
+    )
+    await async_wait_recording_done(hass)
+
+    init_count = sum(hass.bus.async_listeners().values())
+    hass.states.async_set("sensor.uom", "1", {ATTR_UNIT_OF_MEASUREMENT: "any"})
+    hass.states.async_set("sensor.uom", "2", {ATTR_UNIT_OF_MEASUREMENT: "any"})
+    hass.states.async_set("sensor.uom", "3", {ATTR_UNIT_OF_MEASUREMENT: "any"})
+
+    await async_wait_recording_done(hass)
+    websocket_client = await hass_ws_client()
+    await websocket_client.send_json(
+        {
+            "id": 7,
+            "type": "logbook/event_stream",
+            "start_time": now.isoformat(),
+            "entity_ids": ["sensor.uom"],
+        }
+    )
+
+    msg = await asyncio.wait_for(websocket_client.receive_json(), 2)
+    assert msg["id"] == 7
+    assert msg["type"] == TYPE_RESULT
+    assert msg["success"]
+
+    hass.states.async_set("sensor.uom", "1", {ATTR_UNIT_OF_MEASUREMENT: "any"})
+    hass.states.async_set("sensor.uom", "2", {ATTR_UNIT_OF_MEASUREMENT: "any"})
+    hass.states.async_set("sensor.uom", "3", {ATTR_UNIT_OF_MEASUREMENT: "any"})
+
+    msg = await asyncio.wait_for(websocket_client.receive_json(), 2)
+    assert msg["id"] == 7
+    assert msg["type"] == "event"
+    assert msg["event"]["events"] == []
+
+    await websocket_client.close()
+    await hass.async_block_till_done()
+
+    # Check our listener got unsubscribed
+    assert sum(hass.bus.async_listeners().values()) == init_count