Can a spider fang fall off when bitten?

I don't know if I was bitten by a spider. I felt a sharp pain on the ball of my fit when I was on my bed, and I found that a small clear claw shaped projectile was poking me. There was a small dot where it d my skin. It's about the size of a third of a staple. Is this a fang of a spider? There weren't any around when I looked.