Use a 9/16" socket to cover the bolt head, hold it with vice grips, drill the head of the bolt through the center of the socket, no metal shavings flying all over, pop the head of the bolt off, then remove the rail. With the rail upside down and the shank of the bolt sticking out, you have something for the vice grips to get a hold of, then drip a drop of cutting thread oil down the shank of the bolt. Once thats done, try tightening the bolt first, then loosen it, work it back and forth, if it's going to come out, it'll come out then, if not then it'll break off at the threads. If it breaks off, not a big deal. Strip the cloth off the rail, you're going to have the table recovered anyway. Pull the cushion loose from the bottom of the rail enough so that you can get into the cavity where the nut plate is. The bolt is not going to be broke off flush to the anchor nut, so in order to remove it you're going to have to cut off the protruding shank, do that with a metal cutting blade on a Dremel power tool. Slide the blade between the wood and the nut, cut the shank of the bolt off, then remove the anchor nut. Replace it with a new one, or drill the old one out and re-tap the threads, then replace it, repair done.