I originally added the following while this trope was in YKTTW. I just recently watched T2 again and found I was mistaken - it never happened, so I'm deleting it.
Subverted in Terminator 2. John, Sarah and the T-800 are fleeing from the T-1000 in the hospital. After they enter the elevator, Sarah pushes the "Door Close" button. The doors close just before the T-1000 gets there, but it opens the doors with its metal arms.