Can a creditor sell a debt? I don't know why not. The automatic stay prevents collection actions against a debtor, not other actions a creditor could take.
And no, a primary homestead can certainly be taken if the mortgage is not paid. Because it's exempt means something completely different.
Lenders sell notes all the time! It has nothing to do with the automatic stay, which prohibits collection efforts.
As to whether "they" can take homesteaded property, they can if you don't make the payment and are able to obtain a "lift stay" allowing them to proceed with foreclosure.
Hope this perspective helps!
As my colleagues have stated there is nothing that prevents a creditor from selling your note while you are in bankruptcy.
With respect to the motion for relief from stay, the lender is seeking relief from stay so that foreclosure proceedings can begin or continue. Usually this is because you are not making your mortgage payments since filing and/or you are not making your payments to the trustee and the lender does not believe it is adequately protected.
In this circumstance where a secured lender is seeking relief from stay your homestead, nor any other exemption, has nothing to do with whether relief will be granted
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You didn't say whether your wife has an attorney. If she doesn't, she should. You also didn't say whether she filed an objection or any other response to the Motion for Relief from Stay. If she does nothing the lender will get the relief they are seeking and will be free to begin or continue with foreclosure proceedings.
The new party has only the same rights as the previous party. Therefore if automatic stay is in place it will apply to whoever owns the debt. If the relief from automatic stay is granted, the new creditor will be allowed to proceed with collection efforts.
More importantly, if a motion for relief of automatic stay is filed, respondent has 11 days (plus 3 days if served by mail or electronically) to file an opposition to the motion. If no opposition is filed within the timeline, then the motino is considered unopposed and relief from automatic stay is granted without any hearings.
To file opposition, one has to call the clerk of the Judge handling the case and request a hearing, then promptly file the opposition along with declarations & notice of motion, which must be served on the interested parties.