Many games that do this will essentially choose a client to become the host. In doing so, the clients' state is the new authority.
How you implement this is rather dependant on your preference. You may wish to support some kind of lobbying system - where each client can register it's game session ID and state that it is looking for the new host, and the matchmaker service can match the client's up. Otherwise, you would be best implementing a peer to peer solution, either with predefined fallback hosts by the original server (so if host is dropped, the clients have a list of who to try, in priority order) or deal with the new host when the situation arises. In the case of the latter, it will require the clients to be aware of "some" connection data about the other clients, whilst having a matchmaker would remove this dependency.