There are many ways to skin a cat. And many ways to buy a home. Not having all the information, I frankly can't give you a good solid reasoned approach as to how the people you refer to could buy a home, following a foreclosure. Likely the people in question have not shared all their information with you.
If you lose a house to a lender, you will have serious credit issues--which most likely would keep other lenders from giving you financing to purchase a new home. Meaning that most people would NOT be able to buy and would most probably become renters for some few years. If they ARE able to buy, there would have to have been some cash down payment hidden under a mattress or in the private account of a family member or spouse.
it is not as easy as you may be seeing , they may get away with it for the short term, but the bank always wins...
If you have good credit with the bank get a loan on a home up for sale, tell the bank it is an investment property, get a loan, buy. Now is when you get behind on your smaller home and let the bank have it after all you have 2 loans with them now, so let them have the house you don't want.