The costs to a person who does not know when to quit can be enormous. In economics it's known as sunk cost fallacy, though the costs are more than financial. While we recognize the fallacy almost immediately in others, it's harder to see in ourselves. Why?

There are several powerful, largely unconscious psychological forces at work. We may throw good money after bad or waste time in a dead-end relationship because we haven't come up with an alternative; or because we don't want to admit to our friends and family, or to ourselves, that we were wrong. But the most likely culprit is this innate, overwhelming aversion to sunk costs.

Sunk costs are the investments that you've put into something that you can't get back out. They are the years you spent training for a profession you hate, or waiting for your commitment-phobic boyfriend to propose. They are the thousands of dollars you spent on redecorating your living room, only to find that you hate living in it. Once you've realized that you probably won't succeed, or that you are unhappy with the results, it shouldn't matter how much time and effort you've already put into something. If your job or your boyfriend have taken up some of the best years of your life, it doesn't make sense to let them use up the years you've got left. An ugly living room is an ugly living room, no matter how much money you spent making it so.

This is a good decision making framework:

Recent research by Northwestern University psychologists Daniel Molden and Chin Ming Hui demonstrates an effective way to be sure you are making the best decisions when things go awry: focus on what you have to gain by moving on, rather than what you have to lose.

When people think about goals in terms of potential gain, that's a "promotion focus," which makes them more comfortable making mistakes and accepting losses. 

When people adopt a "prevention focus," they think about goals in terms of what they could lose if they don't succeed, so they become more sensitive to sunk costs. This is the focus people usually adopt, if unconsciously, when deciding whether or not to walk away. It usually tells us not to walk away, even when we should.

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When we see our goals in terms of what we can gain, rather than what we might lose, we are more likely to see a doomed endeavor for what it is.

Do you think sunk cost fallacy has its psychological underpinnings in choice-supportive bias? 

http://pandawhale.com/post/2747/behavioral-biases-lead-to-poor-decisions

I think so. Both involve clinging to something we should let go of to make the best decision.