Clients don't wait until their lease expires to renew. At % of the lease time (T1), the client sends a unicast Request directly to the server that gave it the address.
If the server responds with an ACK, the lease resets. If the server doesn't respond, the client tries again at % (T2), this time broadcasting to any available DHCP server.
If no server responds by expiration, the client loses its IP and restarts DORA.