# Unstable particles as asymptotic states

In QFT are unstable particles forbidden from being used as asymptotic states in scattering calculations? I ask because the $$S$$ matrix has an $$I$$ term which can propagate the unstable state. Is this term cancelled by the rest of the $$S$$ matrix?

More specifically, let's say we have a system with 2 massive scalars $$\pi$$ and $$\phi$$ with the interaction $$\pi^2\phi$$, and $$m_\phi > 2 m_\pi$$. Clearly then the $$\phi$$ particles are unstable, so can they be used as asymptotic states?