It's out there, but it's not good.
https://www.youtube.com/watch?v=BkCSlIBmRmo
Old innertube tires don't last very long but newer tires would make it a generation or so before they degrade to the point where they can't hold air. But realistically almost nothing in the world is going to last more than a generation or two before it's non-functional so that kind of realism doesn't make much sense in a post apocalyptic tale.