In the context of office and corporate culture, when two men enter a restroom and have to shit, one enters a stall, and the other gets shy and "fakes a piss", opting instead to pretend to urinate and return later for another anonymous attempt at defecating. One can also "fake a piss" if there are too many people shitting, and using a stall will entail crapping too close to other people. It can also be used if someone sees you enter the bathroom before you can sneak into a stall.
"Man, I had to shit real bad, but the managing partner saw me in the bathroom, so I had to fake a piss".
A late realization of urinal anxiety where a man becomes too anxious to piss after he has already stepped up to the urinal so he stands at the urinal with his dick out pretending to pee until the man next to him leaves.
Normally I don't suffer from urinal anxiety but this time I had no choice but to take the urinal next to the big black guy. Once I got there I stood there with my dick out but I was too nervous to piss and it was too late to bail out and go to a stall so I had to fake a piss until he left.