| Is this producing any movement when you waggle the door? My guess is that it isn't, in which case I would say thank goodness it was the bottom stud that sheared not the top one, as then movement would seem inevitable.
A proper fix would be a nightmare as it looks like the door would have to be removed and stripped. If it hasn't caused a problem so far, I would be trying to stabilise the situation rather than carry out a full repair - after all, 99% of cars never require their doors removed in their lifetime.
Plan A would be to fill the gap between the sheared stud and the hole in the hinge with epoxy putty - you can buy this in ready-to-use form from DIY places like in the photo below. You need to have some 'packing tools' ready to help you push the putty tightly into the gap without any voids - things like the wrong end of a (non-eraser!) pencil would be a good pushing stick. This won't do much to hold the hinge to the door, but it will prevent any movement of the hinge and so help the remaining stud survive as long as the car does. If the door ever needs to come off, this will make it more difficult, but then will lightning strike twice?
Plan B, if you have a friend with a machine shop, is to get a custom fastener turned from a piece of hex bar. It looks like there are still enough threads left on the stud to secure the hinge and enough gap around the stud to get a female-threaded boss into the hole in the hinge. But this would be a labour of love, so you would definitely need a friend to do it - if you could find someone to do it for money, they would probably charge most of the cost of a new door! | 
