I think it can continue even without the source server? Like, once I press the Reply button on this comment, it gets saved to my instance (lemmings.world) then it lets all the other instances know, including lemmy.world (where the community is hosted) and slrpnk.net where you are registered.
Now let’s say lemmy.world stops existing, my instance still would let all the other instances it federates with know, meaning you could read my reply on a community that basically no longer exists. Though I’m pretty sure there are downsides to that (like, what if all the mods were from lemmy.world? There’s no admin who can add a new mod).