I did this on Ascension, but it probably works on any new zombie maps and maybe offline split-screen MP. I have not tried to repeat this glitch, but this is what we did:

Game ended, new game starts. P1 paused game. Just before P2's controller timed out, P1 hit pause and options. While on the options screen, P2's controller timed out (went to sleep) which switched control of the pause menu to P2's controller. P2 woke up his controller, chose options, changed sensitivity to 6 (this is probably unnecessary, just go to options) and then backed out of options, and then backed out of the pause menu.

Then, the screen went to P1 solo view. P2 was still in the game but had no screen of his own. His character, Nicolai, was still there and could be controlled. If P1 looked at P2, P2 could see where he was and try to fight, but if you looked away from P2, he was blind to his own actions.

Pause/unpause fixed the issue.

Just an amusing find.