Twilio evangelist here.
If you're placing outbound calls via the REST API and dropping them into a conference when they answer then yes, PersonA would wait indefinitely in the conference call (actually 4 hours since that is the max call length allowed).
What you can do is include the StatusCallback parameter when you initiate the outbound phone call. Twilio will make a request to this URL when the call ends (or is never answered) and pass as part of the request to that URL a CallStatus parameter which will tell you why the call ended.
You can use the value of CallStatus to redirect Person A out of the conference if needed.
Hope that helps.