When borderlines have these kinds of feelings it is often called "parasuicidal" meaning that it isn't exactly suicidal but rather an expression of pain and a wish to eliminate that pain by any means. And when they act on those impulses it is still considered parasuicidal not suicidal, although they do risk misinterpretation and hospitalization for this behavior. That is why it is good to make sure the therapist is clear about the policy and way of reacting so nothing else happens that could be harmful. I have found that being hospitalized against my will is quite traumatizing so I am very careful about avoiding it at all costs.