Suppose you are running a randomized experiment to assess the effect of X, say some training program for unemployed people, on Y, say the chance of finding a job in the coming year. Suppose also that X takes time: maybe it lasts for several months.

Because you randomize, you do not need to worry about self-selection bias initially. But during the course of X, some people will likely realize that X is beneficial to them, and others may realize that they are wasting their time.

As a result, one might expect that among people who drop from the program, there is a higher proportion of agents for which the treatment effect would have been smaller. This might induce an over-estimation bias of the treatment effect.

My questions are:

Is this kind of bias discussed in the literature on randomized experiments?

Does it have a canonical name?

Do researcher try to control for this, and if yes, how?