During the scene where Obadiah paralyzes Tony to steal the mini arc reactor in his chest, we see Tony is wearing a thin white T-shirt, pulled OVER the reactor, perfectly intact.

However, a few seconds later, after he is paralyzed, we see Tony from above; his shirt is now cut around the reactor, exposing it.

The camera switches angles once more so we see him from his left side, but now his shirt is once again intact, pulled over the reactor, at which point Obadiah removes the reactor, cutting the shirt away as he does.