welbutrin is one of the easier ones to stop, since it has a long half-life. Also, it is a weak dopamine and epinephrine inhibitor, unlike the SSRIs (prozac, etc) Still, it should be tapered off. There may be a little discontinuation syndrome- the symptoms of this are a little anxiety, maybe some crying jags for a few days.
I am on Wellbutrin. ( and Prozac) I have not noticed any hair loss from it. Is it a side affect? Stopping cold turkey is really bad. Tell her not to. She should contact her doc. so he prescribe something else if she thinks it isn't doing it's job. My Phsycyatrist changed my meds. till we got it right and she ALWAYS takes you off one slowly and adds another slowly. Much less mental stress!