I am sorry to hear about your situation, finding a place can be difficult and stressful. If you are still living in the property after it is sold at auction or taken back by the lender, you become essentially a "tenant at sufferance." The new owner has to evict you to forcefully make you leave. Usually that new owner - especially if it is a lender - will send someone to verify whether the property is occupied or vacant. The bank hires a Realtor to sell the home and they or another lender representative will attempt to work out something with you for you to leave in a timely manner (usually no more than 21-30 days). You can ask for some cash assistance to help with your moving expenses, that can be somewhere between $1,500 and $3,000 - or it can be $0. If you are not out in the agreed upon time they will evict you.
If the buyer at auction is an investor then anything could happen. They are supposed to approach you the same way as the lender - although they can choose to evict you immediately - but my experience is most problems with the transition occur with an investor purchases the property.
You shouldn't be too worried about coming home and the locks being all changed, although it can happen, they are not supposed to do that. They cannot deny you access to the property without going through the appropriate channel - eviction through the court and that takes around 30 days (give or take a few).
I think it best you continue to pursue a new property. Once the property sells, either going back to the lender or to an investor/new owner, you will be on borrowed time - about 30 days.
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