I thought you might be asking something deeper, but around these parts you never know.I did not ask that right, it was not accusatory! (After all, Zen meshed quite nicely with bushido and the Samurai.)
: )
I emphasized 'who', because in Buddhism the self is illusory. So when you're trying, who is the who trying? a collection of thoughts, mostly memories, some imaginings of other times, possible futures? When the mind is silent does the ego, do you, exist?
Years ago I met a man who was fond of saying, in each of us there are two. One being who we think we are, the ego driven one IMO, and the other our true self which takes more introspection than our fear based primitive mind can deal with. It is that wall of fear that must be breached to see ourselves for what we really are and then changes can be made to the ego driven self. So I guess to answer your question, do we exist when the mind is silent? Yes, I think so, but it is our true self that exists and not in a physical way. Only the ego driven self has a physical presence. 'We" are not here. We are everywhere.