Playing on our minecraft server my friend noticed a skeleton holding a golden sword, we reached a conclusion that the skeleton spawned either with no bow, or with a bow that has a durability of 0. The picture above is a screenshot I took of the skeleton (that sadly didn't survive).

I realized it wasn't an end case bug with our specific server when I saw the same thing happen to youtuber GoodTimesWithScar on his latest video (at 16:05) where the skeleton picked up their iron sword after they died.