You cannot fail a personality test unless the person administering the test wants to filter out specific personality types that are similar to yours, for a process unrelated to the test itself (e.g. employment).

The thing is, most possible personalities seem to be considered undesirable by employers, and so many people simply resort to lying on these tests to present a favourable image to employers (basically: extrovert, conformist, "positive"/upbeat/optimistic, ambitious, responsible etc.). Looks like employers know about this, but don't care anyway, because they think that if you aren't willing to mold yourself into somebody else for the sake of the job, then you don't want the job enough and there are many others who do.

(Disclaimer: I'm an outsider to the employment process and might not know what I'm talking about. My impressions are gathered from job interview advice and job descriptions.)