I left my parking brake on for a few hundred yards and I heard a snap. Now the rear of the car drives very bumpy.

You may have popped the park brake cable out of the backing plate causing brake parts to become loose. Have the brakes looked at soon.

You need to get those drums off & have the brakes checked. It's possible something broke inside the drum brake on one side. I've never seen or heard of it happening, especially after driving such a short distance, but anything is possible!

Can you provide more info? Did you hit a bump? What do you mean by 'drives bumpy?' Does it ride rough, or does it go up and down a lot after you hit a bump, or something else? Can you further describe the snap you heard, and what was going on when you heard it and immediately afterward (e.g., driving 40 mph on a paved road, hit a pot hole, heard a loud 'breaking' sound as if something snapped/broke, and the ride of the car seemed to immediately change to being more harsh/rough)? Have you had any work done recently, such as tires changed or rotated, struts replaced, wheel alignment, or brakes replaced? Did anything else change (e.g., now when you hit a bump, you hear a new noise in the rear)? Were you carrying anything heavy in the trunk or back seat? I had a '99 Corolla for several years, and had zero problems other than a worn out driver's door handle and a couple of cracked windshields. Great car choice!

Your brake shoe may have failed and is getting wedged in your brake drum. I have had this happen to me.

I have heard a lot of descriptions for brake noises but the term hollow does not bring anything to mind. Can you be more specific about it? Does it happen when you stop? Can you apply just the parking brake and see if it happens?

I think you are on the right track with the hand brake/ parking brake. A vehicle can still drive if its slightly engaged and you would notice some sort of burning smell from the area. Try engaging the brake and disengaging the brake a few times and see if it releases completely. There may be an issue with the line causing it to "stick" here and there. Good luck! Cars are complicated but troubleshooting the small things before spending hundreds in labour is always wise!

I to would suspect the emergency/parking brake. Many times because of non use of the EM brake system the cable seizes and when it comes time to change brake shoes they cause problems. There is a flat bar that is part of the self adjuster/parking brake system that might need to be removed to prevent this problem.

I would say one of two things happened. first maybe the parking brake shoes need adjustment. the most common that i see all the time even with newwer cars and trucks, the rear brakes are set up two ways, the type your car uses is the disc rear brakes used to stop the car and then for the parking brake it uses shoes inside the rear of the brake rotor, inside the rotor it gets very rusty and the shoes tend to rust awat from the metal mounting braket it comes on. i see this all the time, when you go to remove the rotor as you slide the rotor off the shoes fall apart and can not go back on, as along as the rotor is not removed it will stay in place, this problem would of occured anyway it would of taken a while longer and then you would of heard noise from rear wheels but it happened sooner due to removing the rotors, its not there fault but they should of called you and told you that you would need parking brake shoes but thought that you may not use the parking brake which is a bad thought in there part. maybe its just an adjustment that need to be made to the parking brake. heres a picture of the rear shoes to show you the metal bracket the shoes come apart from. another thing is that if the rotors were replaced then that explains it more as the old rotors contain rust and build up and that helped make the parking hold bettter.lets hope it just an adjustment.

Pull the drum on the rear left and check all the brake components before you replace anything. Identify what is clicking or if the parking brake is the cause by driving until the clicking is heard and then, while pulling and holding the parking release lever, slowly apply the parking brake and listen for a distinct change in the clicking noise. If it remains the same, your problem is elsewhere in the rear left area.

Bleed the brakes and check the adjustment on the parking brake.