Right. I think I understand now. I think you have a reasonable cause to have misunderstood.
The fact is that, rightly or wrongly, dictionaries do tend to phrase definitions in this way. You're not supposed to read them as logical statements.
So you might see such a dictionary entry for the adjective dead as the following (which I've just made up to illustrate my point):
If somebody is dead, they are no longer alive.
As a logical assertion, this is of course meaningless, but it isn't a logical assertion—it's just meant as a definition. The if-clause is asking us to imagine a dead person, I assume to help us get our heads around the meaning.
1. He was asked to quit.
We don't know whether he actually quit.
2. He was asked to quit rather than quitting of his own accord.
The red part suggests he actually quit.
I am not a teacher.