Universities are big enough, and porous enough, so that they accommodate many people who are "difficult." Some may be Aspberger's Syndrome, the currently popular confessional of the academy. There are alcoholics, drug addicts, OCD, depressives, and sometimes psychotics. The latter is often a tragic story of enormous promise and achievement, but then they are too ill to do their work. Some of these "difficult" people respond well to therapy and medication, others much less so.
There are as well sociopaths (Wikipedia "a pervasive pattern of disregard for, or violation of, the rights of others that begins in childhood or early adolescence and continues into adulthood. There may be an impoverished moral sense or conscience and a history of crime, legal problems, impulsive and aggressive behaviour") and psychopaths (Wikipedia "personality trait or disorder characterised partly by enduring antisocial behavior, a diminished capacity for empathy or remorse, and poor ).")
And many insecure or manipulative or dangerous people (who are dangerous for whatever reason). In general, you may well end up being in the focus of their obsessions and anxieties, just because you happen to have done something--more or less how you get drenched in a rainstorm because you happen to be someplace. Such people may well be unstable, psychologically needy of attention, temporarily or permanently. They may well have strengths, valuable skills, but that does not make them less dangerous. If you are lucky they will send you a note in the middle of the night resigning their jobs. Immediately send a note to the effect that you regret their decision but must accept it, and you will initiate their separation from your institution immediately.
You need to treat these people clinically, trying not to feed their anxieties, although that may well prove impossible. Never assume they are normal, even if they appear to be. See below.
And try to avoid putting these people in contact with clients, students, or others--you cannot rely on them.
It is useful and helpful to refer some to the university health or therapy offices, but sometimes they are in positions where that just won't happen. They may act out in astonishing ways, they may be liars and manipulators, they may organize trouble for whomever they happen to focus their anxieties upon.
Now you have to protect yourself. Usually, it is best to very politely be Teflon for them, their shenanigans having nothing to do with you. Never respond to their emails, and if they want to talk with you, after five minutes announce a pressing engagement. They are unlikely to take your kind counsel, perhaps saying that they know you are against them. It's not nice, but probably they will have to hit rock bottom, offending some powerful person (or creating liabilities for the institution) who will have the authority to do something.
Imagine an opera: La Devoradora (The Devourer), an opera in one act, by Kockadoodle Do, a Japanese composer.
[The homonymic reference to Dora The Explorer is intentional, and reflects Kockadoodle Do's fascination with girls of great competence facing danger. But now the Dora figure [see below on Dora in Freud, and on Devora in the Hebrew Bible] in effect becomes her opposite, "Swiper, bipedal, anthropomorphic masked thieving fox" (Wikipedia). The opera directly engages the audience (much as in Dora) but now they are deceived into helping La Devoradora, the broken fourth wall inverting traditional theater's audience that was more involved with socializing with each other than what was happening on stage. Rather than Dora finding her goal and singing "We Did It!", La Devoradora "finds" a goal she accepts but does not search for. The parallels to Don Giovanni are deliberate.]
As for Dora, here is Wikipedia on Freud on Dora: