Who is bidding
The lender usually bids first, using a credit bid that can be as high as the debt but is sometimes lower. It is called a credit bid because the lender does not pay cash. Investors bid with cash or certified funds. If nobody bids more than the lender, the lender takes the house and it becomes bank owned (REO).
Money left over belongs to you
If the house sells for more than the debt, the costs and any junior liens, the extra money is surplus and it belongs to the former owner. Each state has its own process to claim it, and some of it goes unclaimed. You can claim it yourself; you do not need to give a surplus recovery company a large cut.
Can the sale be stopped or undone?
Before the auction, a complete loss mitigation application sent more than 37 days before the sale, a bankruptcy filing, military protections under the Servicemembers Civil Relief Act (for a mortgage taken out before service began, a sale generally needs a court order), or paying the arrears where your state or loan allows it can stop or delay the sale.
After the auction, many states give no right to buy the house back. Some do: about a dozen states give a clear right to redeem after the sale, and about ten more depend on the type of loan or sale. In court states the judge often has to confirm the sale first. The redemption map and your state page show which rules apply.
You do not have to leave the day of the sale
The buyer still has to follow your state's eviction or possession process, which means notice and usually a court date. A tenant with a real lease is entitled to at least 90 days notice under the federal Protecting Tenants at Foreclosure Act.