These are the elementary particles in our present standard model:
All other "particles" are complicated composites of these.
Rules of thumb:
a) All particles interact with each other in scattering experiments, either elastically or inelastically(= given enough energy, producing a lot of other particles).
b) Particles decay if in their center of mass there is enough energy to break up into smaller mass particles and quantum number conservation allows it. Note we are into the special relativity frame here.
In the table above, stable, non decaying particles, detectable in cosmic radiation are the electron, the neutrinos and the photons, which last with mass=0 cannot decay into anything. See this table for quark decays.
Composite particles can be stable , bound quantum mechanically, and of these the proton is the simplest , proton decay is looked for experimentally , which if found would indicate a new standard model of particle physics ( of which there exist proposals)
The neutron though decays, because at its center of mass there is enough energy to go into a proton an electron and an electron antineutrino , following weak interactions. Unless it is bound into a stable nucleus, quantum mechanically. Nuclei are classified as stable or unstable, in the periodic table of elements, depending on the quantum mechanical solutions of their binding state, so they may decay also ( in addition to interacting and producing cascades of new particles when impinging on the atmosphere at high energies).
So muons also can decay with the weak interaction, into electrons and an electron antineutrino and a muon neutrino, conserving quantum numbers. The probability of interaction in the atmosphere can be calculated using the scattering crossections and the density encountered according to inclination, and the probability of decay also from the energy of the incoming muon. So what will happen first is probabilistic, and the statement you use explains roughly how things go.