Illegal move question

I have an arbitering question. I witnessed a game between two mid level (1600-1800 FIDE) players where one was winning and had 30 minutes remaining and the other had 30 seconds remaining and was losing. The winning player got overconfident and stalemated his opponent. However, the stalemated opponent in significant time pressure did not notice and moved into check. The winning player then checkmated and won with a different piece. He claimed victory. The losing player then claimed it was an illegal position and it was a draw. This game should be adjudicated a win for the winning side correct? Since the second player was in time trouble could he have captured the king and declared a win?

When the first player was stalemated the game was over.

My understanding is that in classical time games position has to be reset to where the illegal move occurred. I'm not sure of this.