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A quasiparticle is more of a useful concept for describing the behavior of systems than it is a distinct object. In the example you cite, phonons are a convenient way of describing how vibrations are transmitted in matter. The fact that phonons are “quantized” is more accurately just emergent behavior from the system of atoms or molecules, a consequence of the fact that the atoms have quantized vibrational states.
As an analogy, consider a ripple in a pond. The ripple appears to be a real, distinct thing. You can describe it with math (as a wave) and predict its behavior. But it cannot exist separately from the water in the pond. The ripple is an emergent phenomenon in water, a quasi-object. It only exists as a collective behavior of the water molecules.
By definition quasiparticles cannot exist in a vacuum.