Vulnerability is not about organizing actions and relationships around weakness. Rather vulnerability is expressing oneself without shame or apology, accepting opposition and rejection by others, and willingness to take risks for one's belief's and values. Said differently, vulnerability is willingness to live or to be in a way that permits bad feelings to be experienced fully when bad things happen or when contact is lost in a relationship. Naturally, to be vulnerable, ego and character defenses need to be working at only a modest level.
Because pursuing modern life from a completely undefended point of view is impractical, is reasonable to speak and think of 'allowing oneself to be vulnerable' on suitable occaisions. Vulnerability will lead to less consistency in responses and expression. This result can be difficult to accept, because most ego ideals include consistency, as do most social ideals, liberal and conservative alike.
Vulnerability is a goal of many traditions of psychotherapy, but in the Reich and Lowen tradition it has a biological meaning. Vulnerability is only possible if automatic muscular armoring is decreased. Trying to live out a role of a 'sensitive person' by being vigilant about emotional matters is not real vulnerability.
Vulnerability is not about manipulating others to limit themselves in ways that protect us from bad feelings, nor is about forming mutual pacts along that line.