Your IP address is stored everytime you post, moderators can also get hold of this information. Not sure whether they can get hold of registration IP, but, if you make a post, they can access that IP, and if you don't make a post - unless your username is really catchy - you don't need to recover the accoutn as it won't have any value. Also, if you do something like edit someone's trust or send a pm, your IP will also be stored.
If their posting style suddenly changes, that's one way to get them. You can prove ownership if you use a static IP that belongs to you but that's not great as you can host openssl and tor exit nodes that give people your IP.
Vpns, tor exit nodes and other masking services can sometimes leave a trace that they belong to that service or can leave a trace that can track you back to the original user (if the user is not intelligent enough to hide that data, IE using a VPN on a regular browser without noscript and other adaptations means your IP can be traced with some simple js code).