How about your character being in the game all the time. Your character will be an NPC when you are not logged in and actively playing. He/ She could obey some simple rules about behavior to automate the actions when you are not playing. The game could be set up to allow all characters to do this.
Hence if you are actively playing the game and causing trouble others will keep track of your characters and what they see you doing. Then when you are not actively runnnig your character there is always the potential that things could happen when you are not ready for them.
This would mimic some of how the modern world deals with these problems. You can get away with things for a while yet when you try to rest you have no where left to go.
This would also be interesting in general as your character could do things when you are not there. If you have not logged in for a while it would be interesting to check in and see what your character has accomplished.