It was my first time contributing the LZ project by running some selfplay games using my shining new GPU. I immediately got one bizarre game played, lasting for more than 500 moves. The program kept filling dame moves, until some big group being captured. I checked the online game list and saw many 500+ move games. So this doesn't seem to be an one-off problem. I wonder how Leela Zero make decision to finish a game.

In most games, Leela Zero will resign if the winning percentage for one side becomes too low.

In some games though, resignation is not allowed in order to make sure that it learns to 'count' in the end, and doesn't resign in winnable positions.
In those cases you simply have to wait for 2 consecutive passes (which is a valid move). Usually the games become quite long, because the losing side will try every move until pass is pretty much the only option