I don't have terms for you, but perhaps another way of looking at it might shed some light...
Looking for something is a dynamic process - its parameters can be rigidly or loosely defined at the outset, but adhering to those parameters may not be the primary need for the individual or any member of the group at any one time.
If a group is looking for drinkable water in the desert, for instance, this would likely be a primary need for every member of that group, taking priority over other needs until they succeed. If they come across water they know to be unsafe early in their search, they're unlikely to stop at this point. But the longer the search continues without success, the greater the chance that members of the group will choose to drink the unsafe water, ignoring safety parameters they believe to be 'currently unattainable' within a survivable time period. After drinking, they may choose to return to the search within the original parameters, or they may discard those 'unattainable' parameters and stop searching.
Beggars can't be choosers. When we sense our life on the line, fear motivates us to fight or flee, but these options are not available here. I don't think it's a matter of widening our definition but more likely narrowing our worldview, mentally fighting or fleeing from information that appears to threaten our chance of survival/success. If it is true that this water is not drinkable, then we still haven't found drinkable water, and our life is still threatened. If the group continues to believe that drinkable water according to the original parameters can be found, then they may die trying to find it. When motivated by fear (of death), it's often easier to convince ourselves that the water we have is drinkable, than that there is drinkable water out there to be found.
The decision we make to ignore parameters at any point in the search depends on what is believed or agreed on as the key motivation or primary need: is it to succeed in finding something, is it to have something, or is it the specific something itself? When our ego is threatened by a failure to find something, sometimes it is easier to believe that what we have found is that something, than to continue believing that the something we are looking for can be found.