Because of stateless UDP nature there is no way to reliably know if remote peer is alive. That is why timeouts are necessary. If no packets are sent during timeout period, then remote peer is considered to be dead. Timeout option should be synchronized both for server and client.
If there were no packets at all during fourth part of timeout, then special heartbeat packet is sent. So VPN connection should be alive all the time, even if there is no traffic in corresponding TUN/TAP interfaces. Beware: this consumes traffic.
Stale peers and handshake states are cleaned up every timeout period.
This applies to TCP connections too: relatively much time can pass until we understand that remote TCP peer is suddenly died and did not normally terminate connection.