If the settlement agreement indicates that your spouse is responsible for those debts and he is to hold you harmless from those payments, if he defaults on those payments, your credit will reflect the failure to pay. The lender, is a third party and they have not relieved you of any responsibility from that debt. Your recourse would be to filed a motion for enforcement/contempt and request an award of counsel fees and any other damages resulting from his breach.
Yes, it makes the other party responsible. No, it doesn't do anything for your credit if they fail. The divorce settlement is ineffective as to creditors of the couple...it merely gives you a right of recovery from the other party.
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Responsible to you, but a hold harmless does nothing to get you out from under the mortgage and responsibility to the bank. If there's a default the bank can still sue you.
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Your agreement with your ex is binding on you and your ex. It does not change any of your legal obligations to third parties. So, if your ex was to pay the mortgage and HELOC and did not, the bank can seek payment from you and your credit can be impacted. Your recourse will be to sue your ex and/or the guardian on the hold harmless obligation in the agreement. That may not help in the short run with your credit.