The answer to this question depends largely on how the results of the test are interpreted. Generally speaking, no one particular set of characteristics is considered "right" or "wrong". Instead, employers use these tests to determine if an individual's traits match up with what they need for particular roles within their organization.
Therefore, there isn't really any result that could be seen as definitively failing a personality test; rather different scores on certain questions can indicate that someone may not have all the qualities necessary for certain positions.