$\textbf{Prisoners in Solitary Cells}$

There are $100$ prisoners locked up in solitary cells. The king gets bored and offers them a challenge. Everyday, he will randomly select and put one prisoner into a special room. (A prisoner may be selected more than once.) This special room has a light and its controlling switch. The prisoner inside the special room can turn on, turn off, or do nothing with the switch. But no other prisoner can see or control the light. On any day, the prisoners can stop this process by declaring that every one of them has been in the special room at least once. If that happens to be true, then all the prisoners will be freed. Otherwise, they will all be executed. Before starting the challenge, the prisoners are given some time to discuss. Is there a strategy to free themselves?