Revenge: The killer's motivation. Except he was murdered in a past form by different people and people who got born again with those souls just counts as Revenge by Proxy.
Reincarnation: Four men murdered a man by skinning him alive over a land dispute in 1868. The victim and the killers were born again. The victim then murdered the killers by skinning them alive, then killed himself to repeat the cycle. Ultimately, the killer is born as a cop resulting in the crimes always going unsolved.