No, there is no 15 minute rule. It's a carry over joke from college, I'm sure.
If you leave, don't expect to get paid, and do expect to get coached, at minimum. Gather together in people's cars. Hang out at a close 24 hour restaurant if one is available. See if anyone has any LOD phone number in their phone, and call whoever they can to see if that person can either get there or call someone who can. When you are able to get inside, everyone will need to do a punch correction for the time they should have clocked in (and would have if someone had been there).
But whatever you do, don't leave and expect to get paid for your shift.