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A cop should OFCOURSE be able to clock off and go do crime. Them getting caught is something different all together though, getting caught youd get charged, suspended, fired etc Theres a lot of potential RP that could come from a corrupt cop. Now we're moving into a more trusting and free flowing RP community then I think we should be able to do this if we want but understand the consequences.
Roleplay over Ruleplay
I think that once a cop clocks off from his duty he should be allowed to do whatever he likes; however, this is a bit unrealistic as this would usually never be the case in the real world.
I think the way cops and criminals are being payed is completely fair, and it's not only about the money, but the experience as well. If you want to pay as a criminal, that's your business and what you're going to earn is mainly up to how you perform and how well you can avoid the police.
Honestly, I don't find what you're saying adding up. Overall, it doesn't make sense for a cop to do criminal activity after clocking off. As a cop that is off-duty, he/she is still 'technically' on duty in a way (because they can still attend to calls and maintain stability when in urgent times). Being a cop involves intensive training and having a paycheck provided by the state. Being a criminal is mostly a high-risk, high reward type of pay. No one is forcing you to do crime. But you can't expect to keep doing crime and never ever get caught. There's no interactions nor any story in that point. Cops get an increase in pay every rank up they get, but no one said it was easy. As a criminal, doing the right crime full-time will get you stacks of money. But you should always expect and be ready to lose money. Logically speaking you don't lose money for being a cop by protecting a state. And regarding the "Should police characters stay clocked in all the time?", It depends on how much the player wants to roleplay as cop, there is no limit to how much one can stay on duty. But there is a limit to how many can be on duty depending on how many civs are in the city. "Is it fair that police get paychecks that help them do criminal activity when not clocked in?", See, in the end it's also up to the cop on how he/she spends his money off-duty, that's why it wouldn't be basically realistic, to do crime off-duty as a cop. The cop CAN do criminal activity, but if he/she gets caught then there will be consequences to the officers position.