2000 dodge neon rear tire locking up?

It's a bottom spring (orange one) and/or a brake pad problem. I have a 2003 that did the same thing. The bottom spring is for some reason mounted under the lower anchor pin from the factory. Water and road salt draining to the bottom of the drum will weaken and cause the spring to break. Sometimes, with OEM brake pads, this will also cause the friction material to separate from the metal backing of the pad, leaving the friction material to move freely within the drum, causing binding. My brake pads and drums were OEM and in great condition when I encountered this problem. A new set of pads and a brake hardware kit ($15) fixed this problem. FYI, take care of it before it locks completely, cause you won't be going anywhere when it does.

What everyone else said about leaky wheel cylinders and brake shoes. The neon is front-wheel drive, meaning that there are drive axles stemming from the transmission into the hub assemblies for the front wheels. The transmission does not drive the rear wheels at all, so no transmission worries this time.

If drum brakes look to see that the rear wheel cylinder on that side isn't leaking, usually this is the cause, if disc brakes you have a bad caliper.

You have a screwed up spring. I have seen this a couple of times. The bottom spring on the brake shoes is stretched by the knucklehead who put them on. How did that cheap brake job work out for ya'?