You may only invoke your fifth amendment right to remain silent if you could be implicated in a crime. From what you describe you wouldn't be able to "plead the fifth." There may be other options available to you such as objecting on relevency grounds if applicable. You may want to run this by a civil litigation attorney. This really isn't a criminal question.
You can't plead the fifth. In a deposition setting the best you can do is put the objection on the record but since there is no judge present to rule, then you answer it after the objection.
On the other hand, you may want to consult with both a civil attorney or a bankruptcy attorney.
The above information does not establish an attorney client relationship nor is it meant to provide legal advice.
If your are being deposed you can refuse to answer the question until the court makes a decision on your obligation, subject to terms. Usually, you are not allowed to object to question in deposition.
If you are in court you can object to the question on relevancy grounds and the judge will tell you whether or not you have to answer. You are obliged to follow the court's instructions.
If you have received interrogatories you can object to the quesiton. You can also seek a protective order in court.
If this is "Supplimental Proceedings" I am sure the judge or commissioner told you that you could refuse to answer questions and to return to court for a decision.
Under any circumstance, you should be represented by a lawyer because your question shows you don't understand the procedure and are lost in the legal system.