If you've ever been to Mexico, one of the most common things you'll see is a shop with Vulcanizadora in big letters by the side of the highway. They're tire repair places that use the vulcanization process to cheaply repair tires.

You can also use the process in reverse to generate useful rubber from a used tire. In the modern world with global supply chains etc. most tire "recycling" is just burning the tires for energy. But, if it were important to get the rubber out because the post-apocalyptic world is short of rubber, that's entirely possible. It wouldn't be cheap or easy, and you wouldn't get anywhere near 100% of the rubber back. But, in a post-apocalyptic world there are bound to be mountains of used tires that you could feed into the process to get some new, fresh rubber.