This is a really interesting question! The truth is that i don’t know and I can’t say I’ve ever really thought about it.
To me, they are multi-cellular so i’d think it would be possible for them to have their cells grow out of control (this is what cancer is, rebel cells). A quick search online isn’t conclusive but it suggests that fungi don’t have a large amount of cell division (this is how our body replaces old cells) naturally. Therefore, the fungus probably doesn’t ever get cancer but i’m not sure if anyone has ever tested this in the lab!