This may work in your situation, get a drill bit about the size of the head and maybe some smaller ones and drill it first with a drill bit the size of the head intill you hit the substance the head is aginst (ex. sheetrock screw and sheetrock) then go to a smaller one half the size or 3/4 the size of the first one. you will get the matterial it is holding in place but then the screw will still be anckered in the other object some times you can use vicegrips on the part sticking out to turn it. this is you last resort, what type of screw is it and what type material is it i am not familiar with the item you listed