Would have been appropriate to make a new thread, but I will answer your question none the less.
What you are seeing is players currently employed in a Detective Agency. Specifically, they have access to this job special:
| 3 | Deputised | Passive | Able to Arrest those who meet the required threshold after defeat |
Simply put, the more crimes a player does, the more of a "bounty" they have to claim by a player working in a detective agency. After the attacker defeats the criminal player, the attacker may sometimes get an option to Arrest instead.