This process is called retreading. In order to retread a tyre, certain processes have to be observed. It takes careful sorting and inspection of the tyres, since only tyres with no damages can be used. Therefore the casings (the inner body of the tyre) are closely inspected for damages to the steel core.
Until about a decade ago, it was still profitable to manufacture retreaded passenger car tyres. They could be sold to the consumer at a very reasonable price compared to the price of a new tyre, because there were considerable savings made by reusing the casing. And therefore pricewise it was a sensible choice for the consumer.