If the cable snapped, your brake would be deactivated. Your problem happens to me often if I wash the car and immediately park it. I try to avoid that if I can. Try to drive it a drop before parking it to avoid rusting the pads and the rotors together.

 

First time it happened to me, I thought I hooked my rear bumper on something in the back of the garage. I now drive and brake after a car wash, and don't use the emergency brake in the garage. Still get a small lock up.

 

Next time park it in gear, and leave the e-brake off after rain or a wash.