If the stud is sticking out, you may be able to put some penetrating lube at the base and then grab the stud with vice-grip pliers and slowly turn it out. Depending on the diameter of the stud, you might also be able to carefully cut a slot into it with a hacksaw blade and then remove it with a screwdriver.
If you remove the whole leg by taking out the remaining good screw, will that expose the broken screw so you can use pliers or vice-grips on it?
If the stud is not sticking out enough to grab or slot, you could drill into it with a small-size bit and use an easy-out (available at hardware stores) to remove it. In the worst case, you can just drill it out (I'd try to use a drill bit just slightly smaller than the stud). If you mutilate the existing threads you may have to rethread the hole, or chase the threads with the correct thread tap. There is also a chance you will need to tap it to a slightly larger diameter in which case, you should first check to see in which thread size and diameter the cones are available...
Since I can't exactly see what you are talking about, (and don't know the size of the screw, bracket, or anything else) the above advice is just my best guess at how to approach this problem. I hope it gives you some good ideas.
Good Luck!
If you remove the whole leg by taking out the remaining good screw, will that expose the broken screw so you can use pliers or vice-grips on it?
If the stud is not sticking out enough to grab or slot, you could drill into it with a small-size bit and use an easy-out (available at hardware stores) to remove it. In the worst case, you can just drill it out (I'd try to use a drill bit just slightly smaller than the stud). If you mutilate the existing threads you may have to rethread the hole, or chase the threads with the correct thread tap. There is also a chance you will need to tap it to a slightly larger diameter in which case, you should first check to see in which thread size and diameter the cones are available...
Since I can't exactly see what you are talking about, (and don't know the size of the screw, bracket, or anything else) the above advice is just my best guess at how to approach this problem. I hope it gives you some good ideas.
Good Luck!