Particle-antiparticle pairs can exist briefly due to their properties, such as quark color charge, which allows combinations like mesons to form without immediate annihilation. These pairs typically last for a short time before decaying due to wavefunction overlap. The discussion highlights that while quarks can combine in ways that seem to violate the Pauli exclusion principle, their color charge resolves this issue. Theoretical stable unions between matter and antimatter isotopes, like Helium-3 and antimatter deuteron, are possible but not fully understood mathematically. Overall, the formation of stable particle-antiparticle unions remains a complex and largely theoretical area of study.