Known patterns for sharding connections on to servers based on teams or rooms?

I'm designing the servers for a system that puts groups of 50 people together. It's important that those 50 people all get routed to the same server, but I need to support a dynamic number of servers, and be resilient to any given server failing without notice.

I can think of several approaches here but haven't been able to find any existing solutions or patterns to follow. Does this problem have a name and a set of generalized solutions?