The usual thing the military worries about is a "kill switch" (a very unlikely sequence of bits) which disables the hardware completely. The idea is that at the beginning of a war, the kill signal is broadcast by the enemy by every means possible which brings all your electronics to a halt.
This can be hidden in an FPGA - for example attached to the input pins or SERDES - without needing to know anything about the application.
Triggering a malfunction is incredibly easy compared to a proper backdoor. A kill signal could also be injected through side channels e.g. a power line, and the kill mechanism could be implemented in many other semiconductors than an FPGA.
