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11 USC 524 (c) provides that:
"(c) An agreement between a holder of a claim and the debtor, the consideration for which, in whole or in part, is based on a debt that is dischargeable in a case under this title is enforceable only to any extent enforceable under applicable nonbankruptcy law, whether or not discharge of such debt is waived, only if— (1) such agreement was made before the granting of the discharge under section 727, 1141, 1228, or 1328 of this title; (2) the debtor received the disclosures described in subsection (k) at or before the time at which the debtor signed the agreement; (3) such agreement has been filed with the court and, if applicable, accompanied by a declaration or an affidavit of the attorney that represented the debtor during the course of negotiating an agreement under this subsection, which states that— (A) such agreement represents a fully informed and voluntary agreement by the debtor; (B) such agreement does not impose an undue hardship on the debtor or a dependent of the debtor; and (C) the attorney fully advised the debtor of the legal effect and consequences of— (i) an agreement of the kind specified in this subsection; and (ii) any default under such an agreement; (4) the debtor has not rescinded such agreement at any time prior to discharge or within sixty days after such agreement is filed with the court, whichever occurs later, by giving notice of rescission to the holder of such claim; (5) the provisions of subsection (d) of this section have been complied with; and (6) (A) in a case concerning an individual who was not represented by an attorney during the course of negotiating an agreement under this subsection, the court approves such agreement as— (i) not imposing an undue hardship on the debtor or a dependent of the debtor; and (ii) in the best interest of the debtor. (B) Subparagraph (A) shall not apply to the extent that such debt is a consumer debt secured by real property. "
So, if there was no reaffirmation agreement, yes, it appears that you could stop paying and let them take the home, without liability for a deficiency if any.