When a replica joins Paxos with an empty log, we don't allow this replica to fully participate in Paxos immediately. Instead, this replica is treated as a non-voting member, meaning that it will not reply to any requests from other replicas. It simply learns those log entries that have been agreed on and tries to catch up the leader. When the catch-up process is done, we re-admit this replica to Paxos and allow it to vote.
If we have a disk failure and want to swap a master machine, we can simply start the scheduler on a new machine with an empty log (and that's it).