Might be a dumb question but please help

[Devin Borders]

My wife and I are wondering about the pre-foreclosure process and how it makes sense if you have equity in your home. For example, we bought our house two years ago for 240k and put 20% down. It has since gone up in value to about 270k. Let's say I lose my job and we blow through our savings and can't make any more payments. If I get a yellow letter or someone knocks on my door saying they can pay off the 186k we still owe, why would I ever say yes? Why wouldn't I put it on the market for a super low price, but still much higher than what I owe? I just don't see how that makes sense? 

We currently bought a subscription to foreclosure.com and are seeing properties that are in pre-foreclosure or even going through the short sale process, but I can't seem to figure out what to do with them. Can someone please explain to me why someone would choose to sell their home for such a low amount when they could potentially get more? Is it just a timing thing where they want to sell fast and are willing to forego thousands to do so? Thanks in advance for any advice!