The American's with Disabilities Act does not prevent a secured lender from exercising their legal rights to property. This law primarily protects the rights of disabled employees. If you haven't read this law, I am posting a link to allow you to review it for yourself. Hope this perspective helps!
There are a lot of questions you raised. Did the lender say they were going to lift stay? Have you already filed? Do you have an attorney? If you have an attorney that person would be the best person to ask your question. If you don't have an attorney it might be a good time to consult with one.
By on disability, I'm assuming you mean collecting government benefits die to the person's disability. Persons on disability do not have any additional or different rights when compared to persons not on disability.
If Chapter 13 is filed, you may be able to keep the home based on the agreed-upon payments in the plan. Chapter 7 is the bankruptcy that buys you time, or will "put off" the bankruptcy, as you put it. Either way, you should definitely consult an attorney before doing anything.
As a side note, I've helped people get loan modifications on their mortgages. That may be a good route to go if your income is from the government and the lender can bank on that income being there indefinitely.
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The ADA does not entitle you to keep secured collateral without paying for it. Yes, the automatic stay pursuant to S362 of the BK Code would thwart the foreclosure sale, however you still need to work out some sort of method of keeping or surrendering the property with the bank. Some jurisdictions have a loss mitigation process, which would enable you to facilitate a loan modification (there are several federal programs which you may be eligible for) If you do not reach out to the lender they probably will file a motion to lift stay to protect their rights.