Debt that is 100% personal to you remains that way.
Further questions to be answered will require a full review of your documents, investment structure and accounts history.
You should talk to a bankruptcy attorney before doing so. If you stop paying, they will eventually obtain judgments against you, and then they can garnish your wages and any other assets in your own name. It doesn't sound like your wife is personally liable for the debt in question, so they could not go after her separate assets, if she has any.
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Your creditors will eventually get judgments against you and, since it appears you are not collection proof, they will attempt to collect your assets and garnish your wages. Depending on your debts and assets, bankruptcy may be an option.
Though we strive to provide accurate legal information in our answers on AVVO, our answer should not be construed as legal advice and it does not create an attorney-client relationship. Our firm only forms attorney-client relationships by written agreement signed by both our firm and the client. Please seek an in-person consultation with an attorney immediately as almost all legal matters are time sensitive and failing to meet deadlines can result in adverse consequences.
If your wife is not on the contract, then there is no liability. You need a good bankruptcy attorney to help you and advise you based on the facts of your individual case.