How Come Mortgage Lenders Don’t Want Foreclosure?

I am refering to if the loan thats due is worth significantly less than the value of the property. So in that case, why would a lender not want to sell this property and gain all of the profits from the sale?
Like in Texas, if the borrower misses 3 months of payments. Property is worth $300,000. Missed payments, plus the entire loan is $250,000. So why would a lender not want to either sell this property at a tax deed auction or sell it afterwards if their were no bidders? Since they would gain all the profits from the property either way.
If they would not want to go through this foreclosure process given my example given, then would it be possible for me to buy their loan from the lender and have the property go into foreclosure so I can reap the profits?
Tell me what I am not understanding please.