Jim may be broke, but either way; he owes me money.
Although Jim may be in a financial crisis, it remains true that he is indebted to me.
If Jim is broke, it implies that he does not have any money. Despite this, the statement suggests that he still owes money to the speaker.
The sentence you provided states that Jim may be broke, but regardless of his financial situation, he still owes you money. The word "either way" is used to indicate that regardless of the possibility of Jim being broke or not, the fact remains that he is in debt to you.
If you need more information about Jim's financial situation, you might want to directly communicate with him and ask about his current circumstances. Alternatively, if you have previously established a formal agreement or contract regarding the money owed, you could refer to those terms to determine the appropriate course of action.
Remember to maintain open communication to clarify any misunderstandings and find a resolution that works for both parties involved.