in the case of a ill 3B and a total roster of 10...
couldn't coach have FLEX hit for DP, and thus DP has left game,
and then sub the DP player in for the ill 3B?
result - Ill girl is out of lineup, and your lineup is reduced to 9, but you don't have to take an out when the 3B bat comes up...
No, once a player has occupied a spot in the lineup, that is the only spot they can ever occupy. A player and their sub may never be in the lineup at the same time.