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On Magician's Academy, this happens to Tanarotte and Suzuho when they join Takuto's regular school... especially after seeing how they act with Takuto. Of course, none of Suzuho's questions got answered.
In The Well of Lost plots, Thursday gets grilled by many characters in the unpublished book Caversham Heights (where she's hiding out from Goliath and Lavosier during her advancing pregnancy) when they find out she's an Outlander. Some of them don't believe she is an Outlander when she admits not knowing things (like "the purpose of alphabet soup"), so she has them leave off their speech descriptors and successfully identifies several speakers in order.
Farscape: Jool and Sikozu got this treatment as newcomers. Neither of them were particularly forthcoming. Crais got this treatment when he deserted, too.
On How I Met Your Mother, the gang does this to poor Victoria about her love life, with the questions thinly disguised as being part of a Truth or Dare style board game.
On The X-Files, Mulder does this to Scully in their very first scene together. It's about five minutes of him grilling her on how she came to be partnered with him, her thesis, her thoughts on the paranormal, and then questions about the case he's working on. It serves to try and throw her off her game and perhaps even frighten her enough to ask for reassignment, but it backfires on him. He finds that she does not back down and has a comeback to his every objection. And thus, the Mulder/Scully dynamic is born, and continues one for the next nine seasons.