Don't sign it, BUT keep making the payments. They are HIGHLY unlikely to foreclose on this lien. Good luck.
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A reaffirmation agreement is a separate promise to pay a debt. If the lender's lien on the property is good, the lender can repo the property if you don't pay. As long as you continue to pay, there is no reason to repo, even without a reaffirmation agreement. Hope this perspective helps!
The cost of recovering an installed HVAC system would likely exceed whatever they might be able to sell it for. They could, however, object to your discharge of that particular debt if they feel they can prove that you knew you were going to file BK when it was installed.
This is a very state-law specific question. Here are the major issues:
Is the HVAC now considered a fixture? Do they have a valid lien? What are their remedies?
The advice of the other attorneys is good, for what it's worth. I would not reaffirm the debt, but until you are certain that there can be no ramifications to not paying, I would continue to pay the monthly note.