I'm on PC.
When the host leaves, 95% of the time I find myself as a new host with 0-2 of the other players joining the restarted wave. (There have been a number of times where the host leaves, and then the group of 4 turns into a solo match for me, usually I'll get all the other players though).
4% of the time I end up joining another host.
1% of the time I'll get your experience where I get kicked to the multiplayer menu.
Sounds like you are experiencing an unusual issue.
I'm guessing it determines that somebody else should be the host, but you end up having trouble communicating with their PC so it boots you to the Main Menu. Traditionally, firewall settings were causes of peer-to-peer connection issues. I have no idea what the source of your issues are.
