I agree the Drow would get significant penalties in daylight. The illithids have a huge presence in the underdark so it is quite realistic that Drow are being kidnapped by them. Probably easier for the illithids to kidnap Drow tbh.
Except Illithids and Drow have a long history of cooperation (allying would be too strong a word.) It would be quite unusual for Illithids to take a drow as a slave or host for their parasites. Not unheard of, but very unusual because while the Illithids consider themselves superior to all other races, they 1) consider drow to be closer to being on equal terms than other races are and 2) they fear drow reprisal.
