Following my last question (thanks @crip659 !), I was able to put the nut back on.
However, now it is stuck at this kind of middle level where the threads stop. When I removed the whole thing from the exhaust fan, the nut and the washer were stuck together.
How can I bring them closer again? I tried turning in every direction but it doesn't change. I don't want to go too hard and break the bolt.