If you mean the acorn-shaped lug nut, I am guessing someone welded the stud to the inside of the brake drum rather than swedging it in place. Depending upon the quality of the welding job, they sometimes break loose when trying to remove the lug nut. If you have access to an acetylene torch and don't care about the paint on the wheel, heat the nut until red. Allow to cool and then try backing it off. The heat will cause the lug nut to swell and loosen its grip on the stud.
You might also try cocking the lug nut wrench at an upward angle to put pressure on the stud against the brake drum hole it exits. That might bind it enough to spin the lug nut loose.
On the other hand, if there is really an open face hardware store hex head nut instead of the correct acorn lug nut, spray some penetrating fluid in the center of the stud so that the fluid runs down the stud's threaded shank. Do that a couple times a day for a few days. Then try to back off the nut, once again cocking the lug wrench at an angle to put pressure on the stud.
Do yourself a favor and have new studs swedged in the brake drum to avoid future problems like this.
Marshall