Was in a game earlier. By pure chance, I accidentally clicked on the Characters menu the millisecond our Barracks got destroyed. This happened:
Throughout the remainder of the match, I still had access to Officer, Rocket Soldier, and McFarland. The units I could not afford (had less than 1000 credits when we lost the Barr) disappeared the very next time I opened the Characters menu.
I just hope someone doesn't find out how to exploit this to continue using SBH and Hotwire/Technician.