I love Rust, probably one of my favorite games ever. However, playing on a normal server is pretty much a full time job. It seems that people either move onto something else or become entirely consumed by the game. Any games that are like Rust but aren't like that?
If it doesn't have to be an FPS style... you could try MyHordes
Its ... weird and hard to explain.
Its an online post zombie apocalypse multiplayer co-op survival "board game"(?) that takes place in real time. It is expected that the "town" and all its "citizens" are going to be wiped out. But before then your goals can be to get personal achievements (there is a list of them and how many times you've achieved them on your Soul page), role-play (either working for or against the survival of citizens and the town), outlive all the other citizens (through zombie attacks, their own fatal mistakes, or your own help), or try to coordinate the town's growth and defenses to survive for as many days as possible.