The neutrino is a good example of a particle that almost doesn't exist. They are produced in solar reactions in spectacular amounts. Trillions of them are flitting through you right now as if you don't exist. You'd need a light year block of lead to ensure you could stop one. Mind-boggling amounts of them have to pass through our detectors to see even a single interaction.
Simply put, the particle physics does not have to behave nice so you can sleep well at night.