rather than team penalties so the players just sit in the box for 5 minutes while the rest of their teams play normal 5 on 5. Sometimes one player may get a 2 minute minor for instigating or roughing but if this was a line brawl at the beginning of a game that’s probably not the case.
Any in any case, one team will never have fewer than 3 skaters (not counting the goalie) on the ice at a time. If a team is down to 3 skaters and takes another penalty, they would still have 3 skaters and the new penalty won’t begin until another expires.
At least, that’s how it works in the NHL and I think all of North American hockey. Who knows what crazy things happen in Europe/Russia.