So no particle exists unless it interacts with another. I personally think the whole universe is one big interference pattern. Perhaps the interference fringes have become uncoupled at high energies and appear to be moving about independently, but originally I think they came from the interaction of more energetic particles. I think we're just beginning to understand how particles such as photons can be split and yet share some properties over large distances, almost as if they are the same particle. Perhaps they exist in the same space in a higher dimension, and we see them in 4 dimensions like the surface of water would see our fingers if we immersed them: two separate cross-sections, even though they are attached to the same hand.

If a particle never interacted, it would not be a part of this big mess we call a universe. On the other hand, nothing can escape from the event horizon that envelops this universe, so I think even the most scarce particle is going to interact at some point, and so its existence is going to persist rather tenaciously. Close your eyes, the universe will still be there when you open them again.