According to the description of the situation, the first answer is that you may be prosecuted. The following is a detailed explanation of this conclusion:

1. The debt is more than 9,000, which is four months overdue. Overdue repayment is a violation of the credit card contract. According to the provisions of the credit card contract, the bank has the right to take legal measures to recover overdue debts.

2. Received a call from a “law firm” to demand repayment. If someone claiming to be from a law firm calls you to demand repayment, it may mean that the bank has entrusted the overdue debt to a law firm or debt collection agency for collection.

3. Calls from debt collection law firms may be legitimate. Law firms, as institutions specializing in legal affairs, are one of the legal collection channels. However, it should be noted that to verify the identity of the other party to prevent fraud, you can ask the other party to provide relevant evidence to prove their identity.

Summary: Based on the above situation, if you owe more than 9,000 yuan four months overdue, you may be sued. Therefore, it is recommended to pay off overdue amounts promptly to avoid further legal disputes.

Extended information: Overdue credit card repayments will cause damage to the credit record, and the bank has the right to take legal measures to collect or sue. The longer the delay in repayment, the greater the negative impact it may have on your personal credit record. Therefore, it is recommended to communicate with the bank or relevant collection agency as soon as possible in case of overdue payment and formulate a repayment plan. Timely repayment is one of the important factors in maintaining a good credit record.

Supplementary information: If the question does not mention whether there has been communication and negotiation with the bank about the overdue debt, it can be assumed that no communication and negotiation has been carried out before. In actual operation, actively communicating with the bank to understand the specific situation and reaching a repayment agreement as much as possible may reduce the risk of being sued.

The above are answers to questions and are for reference only. The specific situation needs to be judged based on the actual situation. If there is a legal dispute, it is recommended to consult relevant professionals or legal institutions.