Official source

Quick answer

[Official] Yes, Big Walk autosaves group progress on the host's game. The host is the keeper of the save, so the same host must start a returning session when the group wants to continue from the same point.

Official source

How saving works in Big Walk

  1. Choose a host who is likely to attend future sessions, because that player's game keeps the group save.
  2. Have the host start the session and load into the world before guests connect.
  3. Play normally; Big Walk saves the group's progress automatically on the host's game.
  4. For the next session, have the same host start the saved journey before the group joins.
Official source

Can you transfer a Big Walk save to another host?

[Official] The reviewed FAQ identifies the host as the keeper of the save and does not document a way to transfer that save to another player. Do not assume that starting a session with a different host will continue the original host's progress.

Official source

What happens when the host leaves?

[Official] When the host stops the session, every guest is disconnected. To continue the same journey later, the original host needs to host again before the other players reconnect.