When is foreclosure a good idea?

Please provide more information about your situation. Are you talking about foreclosure on your personal residence? Or do you own investment property that is upside down and has negative cash flow that you want to let go of? 
Or you are the lender and the borrower is not paying the loan and you are considering foreclosing? Which is it?
If you are referring to the property that you own, foreclosure should always be last resort. If you own a property (residence or investment) that you are unable to meet your obligations and is upside down the first thing you need to consider is loan modification. Many lenders are willing to work with distressed borrowers and modify their loan terms to make it more affordable to keep the property. 
The next thing to consider is short sale. You sell the property for the amount that is less than the balance owed to the bank. Again, many lender would be willing to work with you. They don't want to take your property and would rather accept less and write off the rest.
In most cases you should be able to solve the problem using one of the above. If not - talk to the lender about "deed in lieu of foreclosure".  With this option you voluntary transfer the deed to the lender.
If none of the options described above works, then eventually lender will foreclose on the property and sell it to recover their loan. This is the decision that banks makes - not you. Be responsible, you have an obligation to pay the loan and if you are unable to do so - with with the lender on possible solution and don't just ignore it and wait until the foreclosure takes place. 

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