The authors state that you should take neither an agressive or passive approach to this behavior, but an assertive approach. They give examples of the assertive approach, including knowledg of the issues and not letting the person's traits drain your energy. The book explains these approaches in much detail.
Borderline Personality Disorder is:
A pervasive pattern of instability of interpersonal relationships, self-image, and affects, and marked impulsivity beginning by early adulthood and present in a variety of contexts, as indicated by five (or more) of the following:
(1) frantic efforts to avoid real or imagined abandonment. Note: Do not include suicidal or self-mutilating behavior covered in Criterion 5.
(2) a pattern of unstable and intense interpersonal relationships characterized by alternating between extremes of idealization and devaluation
(3) identity disturbance: markedly and persistently unstable self image or sense of self
(4) impulsivity in at least two areas that are potentially self-damaging (e.g., spending, sex, substance abuse, reckless driving, binge eating). Note: Do not include suicidal or self-mutilating behavior covered in Criterion 5.
(5) recurrent suicidal behavior, gestures, or threats, or self-mutilating behavior
(6) affective instability due to a marked reactivity of mood (e.g., intense episodic dysphoria, irritability, or anxiety usually lasting a few hours and only rarely more than a few days)
(7) chronic feelings of emptiness
(8) inappropriate, intense anger or difficulty controlling anger (e.g., frequent displays of temper, constant anger, recurrent physical fights)
(9) transient, stress-related paranoid ideation or severe dissociative symptoms
Further information on Borderline Personality.