You can depolymerize rubber. but the process depends on the polymer type and on the crosslink type. A more common approach is to pyrolyze the rubber. That is, to heat it up in a non oxidizing atmosphere. This will convert the polymer to monomers and oligomers of the base polymer. Whichever approach you use, it will get very dirty.
A more common approach with rubber is to have it ground very finely. Then you use it in a rubber compound as a filler. You can use the reground rubber this way, but it is usually a nonreinforcing filler. The more you use, the weaker physical properties like tensile and modulus will get.
Hope this helps.