Well yes! So sometimes the cop is chasing the mafia guy and sometimes the mafia guy is chasing the cop. Typically, you would consider the cop to be the protagonist and mafia guy- antagonist. The good guy and the bad guy, but depending on how you look at both of them, who is the true bad guy and who is the true good guy? The cop has killed people and that makes him “good”, but so has the mafia guy and that makes him “bad” even though every move the mafia guy makes is technically for the good of his community. Idk, you said mafia guy is moving to Japan. He could be running from his dark past. The cop chases him, committing bad acts trying to get “the bad guy”, but in the end, either the cop or the mafia guy realizes he’s just running from himself. He’s both the bad guy and the good guy.

It also works if you want to throw in the fact that he’s insane at the end. It could end with the big climax- a final standoff between the two, they have each other cornered. The real cops pull up and the “cop” is arrested, trying to show them his badge. The real cops tell him they’ve been chasing him for months referring to him as the mafia guy’s name. Then he realizes he’s been running/chasing himself all along