buy house after foreclosure

Can a person foreclose on her house, and after doing that using retirement money to buy another foreclosure?

My mother in law wants to foreclose on her house that has a balance of $100,000 and she wants to buy another foreclosed house for $20,000 in cash. Can she do that without problems from the lender?

If she plans to buy her new home for cash, no one will know.
Since if she is paying in cash – she will not need a loan.
No credit check will be performed – whatsoever.
/

buy house after foreclosure