Think in terms of a courtroom -- prosecutors cross-examine EVERYTHING.
This is a role some residents take up in the system that is characterized by criticizing, generally negative/pessimistic, maybe sarcastic, behaviors. Prosecutors may blockade behaviors and activities, possibly call people names, and are generally hypercritical. Due to these behaviors generally being "socially unacceptable", internal prosecutors can attract a lot of negative attention in the system.
However, prosecutors are guardians and protectors, too. In a more positive light: they play devil's advocate, they'll look over your ideas and point out the flaws so you can fix them, they protect from sly and manipulative mental/emotional abusers by questioning everything and everything and constantly reality-testing. It's like having a critic in your head — if you can give them the jobs suitable for critics, it can be a very fruitful relationship.
To ease internal relations, take what they say with a grain of salt. Ask them to chill out if they're being to assertive/aggressive with criticism. But they're there to protect you. If they say something you don't like, ask why — they often have a good reason.
Internal prosecutors can try to interfere with relationships (internal & external) because they are afraid there's a hidden agenda, and sometimes they're right.
They're your reality check.
When not co-conscious, internal prosecutors can be perceived as a self-critical train of thought, questioning everything you do, how you do it, why you're doing it, etc.