Apparently there was some research done on what happens when people try to cheat MBTI tests.
This research investigated whether respondents rely on their stereotype of members of a particular occupation when attempting to fake personality questionnaires to gain employment in that occupation. The subjects' test profiles when attempting to fake the MBTI to gain employment as psychiatric nurses were compared to those of actual psychiatric nurses as well as with the subjects' profiles under either the normal administration protocol, instructions to complete the test to give the best general impression of themselves, or instructions to describe a typical psychiatric nurse via their test responses. Although the subjects failed to imitate the profiles of psychiatric nurses, their responses were highly sensitive to these instructional manipulations. The data suggested that subjects' faking strategy is based on their stereotype of members of the target occupation. Although there was a significant difference between the subjects' fake-job and stereotype profiles, these two conditions yielded identical typologies. In addition, the Euclidean distance between these two profiles was significantly less than that between the fake-job profiles and those obtained in any other condition.
I don't actually know what the bolded sentences mean, and reading the article itself will cost money so I'm not going to do that. So...