It will prompt the agent to generate a response to continue the conversation with whatever context it has from its instructions and conversation state.
That’s a fair point, I’m sure this has come up before (it has, here). The advice previously has been to shut down the room from an external source, for example listening for a participant disconnect webhook on your server and terminating the room using the Room API when the number of participants is 1 (or starting a timer and terminating the room when that expires). There’s also an associated open issue: Feature Request: Auto-close room when only 1 participant remains for N seconds · Issue #4753 · livekit/livekit · GitHub.