I have got a few examples::
- For instance when someone buys something and it turns out that it wasn't worth it, and this person tries to convince himself that he made a good choice or that the product he bought is actually worth it (he cannot accept that he lost money in that process). That might be at the cinema when the movie is bad and you stay until the end because you've paid for it.
- The other example is when someone made something which is likely to end badly, but the fact he began to follow this way lets him prefer to make an error later than go back on it immediately.
It seems to me that both are the same. I learnt the term for this phenomenon in a philo/psycho course at school a few years ago, I think the term is similar to "heuristic of loss", or maybe "bias of loss", but my search engine doesn't know that, so it is likely to be something else. It is possible that I mix up terms and concepts.
Not certain this is what you are thinking about, but this sounds a lot like the idea of "sunk costs", which is a form of loss aversion.
Sunk costs means that you tend to overvalue the effort you have already put in to something (time, money, etc), and often are willing to put in more effort to try to rescue what you already put in, even though the additional investment (again: time, money, etc) is not worth it. Often people make poor decisions (financial, relationship, etc) because they feel like they have "put too much in" to it.
A related concept is the Endowment effect (first mentioned in another answer by JoaoBotelho). Like sunk costs, some of the endowment effect can be explained by loss aversion, though some experiments have also shown a smaller mere ownership effect which is not also explained by loss aversion. These effects describe how people tend to put more value on things they own or have some relationship to (for example, an object held versus an object at a distance) versus things they do not.
It's an extension of the Endowment effect:
In psychology and behavioral economics, the endowment effect (also known as divestiture aversion and related to the mere ownership effect in social psychology1) is the hypothesis that people ascribe more value to things merely because they own them.
I guess you might be looking for commitment principle in social psychology? I think I have heard about it in only social relationships so far but why not? according to this prinsiple, we are likely to commit in our relationships. It is harder to turn back from an action after you started.