They go to quantum fields...their version of heaven.
Actually there are virtual particles. In the positron-electron annihilation Feynman diagram, a virtual photon is created and then quickly becomes a positron-electron pair again. This virtual particle was invented to account for the conservation of energy during the process. Without it, the energy audit did not balance.
While this making up particles to balance the books is not very satisfying, the alternative is even less so. In the alternative way to conserve energy, they imagine the conversion process happens so quickly that the two particles can "borrow" the energy and then give it back before the universe knows it was gone. See what I mean...we are bordering on the silly here. [As an aside, this is not the only place they play this silly little borrowing game. So-called quantum tunneling does the same magic with energy.]
Particles, sub-atomic particles, do not contain nucleons. In physics, a nucleon is a collective name for two particles: the neutron and the proton. Both of which are hadrons as they consist of quark triplets. The quarks are the particles. They make up nucleons, they do not contain them.
The electrons, also members of the same Standard Model family as the quarks, flit about in their orbitals that envelop whatever the quarks make up. And the little guys, the neutrinos, hide in among the quarks inside the nuclei.
A typical disintegration of a particle results in photons being released. This means the mass energy of the original particles has been converted into energy, which took the form of photons. But both electrons and neutrinos have long lives; so they are not prone to spontaneous disintegration. And quarks can't live alone. They can only exist as triplets in hadrons, like protons and neutrons. As hadrons, quarks are also long lived.