I have -4 Tactical Officers, they get killed on missions and failed raids. It seems strange to have a negative number of Tactical Officers. I think once you reach 0, then it shouldn't be possible to lose anymore officers.

Further more i feel the mission should not be allowed to be performed either. Like Greyed out

i don't think there is anything that have a chance to lose only tacts, thou i'm not that well versed to be sure
so when lose random crew pracs, it can just check for all crew and exclude any type that reached 0

and if you got 0 of all crew, then it get grayed

haha, good luck getting new redshirts to join your crew. Its almost like they need to pass the gauntlet from Indiana Jones: The Last Crusade just to get on board.

Just tell them the penitent man will pass.

But in all seriousness, it should be capped at zero.