Injuries to catchers

This has probably been answered a long time ago, but my #1 catcher is out for 4 games and my back up is Hershberger. Can both of my catchers get hurt at the same time? Who catches then? And does this just become a defensive nightmare?

The last catcher on your roster becomes bullet proof when the other(s) are injured.

No, if Hershberger is the only non-injured player who can catch, he will be bulletproof until your #1 returns.

However:
If your backup catcher is in your lineup at another position, HAL won't move him to catcher to fill the injured catcher slot.