Everything is made from rubber and plastic now. Bread? Plastic. Meat? Rubber. Vegetables? Plastic. Milk? Rubber. Chewing gum looks like rubber, but is actually plastic.

because it is: https://en.wikipedia.org/wiki/Gum_base

It is plastic, though. The exact formulas tend to be proprietary, but they use a plastic rather than a natural gum base unless explicitly stated otherwise on the packaging. Even a lot of the 'natural' brands still use a plastic base.

A podcast years ago. A cursory search confirms that modern chewing gum has a "gum base" that contains food safe plastic polymer. Old school ones are made from gum from trees, but that hasn't been economically viable for like a century.

Most of it will decompose but other parts either gets buried in a landfill or gets burned where the smoke goes into the sky and turns into stars.