Generally, if a user gains a reputation-based privilege, the user will lose it if they later fall below the required reputation.
I've found that this has one major exception in chat. Users without enough reputation to chat are not allowed to have a custom username or custom avatar; their chat username is their generic "userXXX" username, and their avatar is the standard one given to deleted or nonexistent users. However, if they later gain enough reputation in chat but later on lose it (including via suspension), their username and avatar are displayed permanently (or as long as their current chat profile exists); they are not reverted back to the generic ones. In other words, if at any point a given chat profile had 20 reputation at the time it was synced, it will permanently retain avatar and username rights. Here's an example chat profile.
Why was the decision made to implement it this way? Why not revoke their custom avatar and username privileges on chat if they later lose the reputation? This effectively allows suspended users to troll chat rooms with offensive avatars until a moderator deletes their chat profile. (Thankfully, if the user recreates their chat profile, it won't have those privileges.)
(I'm not reporting a bug or making a feature request to ask that it be changed; I just want to know why it's implemented this way.)