When someone has a mortgage on a home and they miss at least 4 mortgage payments then the foreclosure process usually begins after 4th missed mortgage payment.
Then during that foreclosure process the person who took out the mortgage usually has the option of paying those back mortgage payments off plus any additional court costs and other fees to keep the house.
If the person cannot pay back those back mortgage payments and other fees to stop the foreclosure then the bank will serve you with papers to be out of the home within 30 to 90 days depending on what's stated in the foreclosure and eviction notice.
Then once you've been foreclosed on and the bank now has possession of the home once again the bank could immediately put the home on the market again and list it as a foreclosure and sell it at an auction or they may wait awhile so they can evaluate the home and have it cleaned out.
I've seen some foreclosed homes get sold at auction a few weeks after it was foreclosed on and then some took a few months to be sold at an auction.
That's how some banks will do the sale of the foreclosed home they'll auction it off while others may list it back on the market for sale and then someone will have to get a mortgage from another bank to pay that bank in full for the home.