Stating the obvious here but the players can quickly recreate the game that was interrupted by doing the same moves.
Customize starting position

You have to be a premium member, but there's a live analysis board that allows you to load up any PGN. Danny talks about it in this video:
https://www.youtube.com/watch?list=PL-qLOQ-OEls4uS2rARp8DAeId7AP7Tt06&v=hSCa2sfr4Lc
Or if you kick over to V3 from your home page, it's part of the V3 tour. Let me poke aroumd and see what else I can find...
EDIT: A premium member has to be in charge of the board, but can invite anyone. Couple of clicks to load a game from your archive.
Why don't is possible set a custom start position loading PGN? I know this should be only allowed in "unrated" game, but it can be very usefull. For example when a match is finished on time by accident and players want to finish the match, or many others situations...
Thank you.