The zodiacal cloud is one of the largest structures in the solar system and strongly governed by meteoroid collisions near the Sun. Collisional erosion occurs throughout the zodiacal cloud, yet it is historically difficult to directly measure and has never been observed for discrete meteoroid streams. After six orbits with Parker Solar Probe (PSP), its dust impact rates are consistent with at least three distinct populations: bound zodiacal dust grains on elliptic orbits ($alpha$-meteoroids), unbound $beta$-meteoroids on hyperbolic orbits, and a third population of impactors that may either be direct observations of discrete meteoroid streams, or their collisional byproducts ($beta$-streams). $beta$-streams of varying intensities are expected to be produced by all meteoroid streams, particularly in the inner solar system, and are a universal phenomenon in all exozodiacal disks. We find the majority of collisional erosion of the zodiacal cloud occurs in the range of $10-20$ solar radii and expect this region to also produce the majority of pick-up ions due to dust in the inner solar system. A zodiacal erosion rate of at least $sim$100 kg s$^{-1}$ and flux of $beta$-meteoroids at 1 au of $0.4-0.8 times 10^{-4}$ m$^{-2}$ s$^{-1}$ is found to be consistent with the observed impact rates. The $beta$-meteoroids investigated here are not found to be primarily responsible for the inner source of pick-up ions, suggesting nanograins susceptible to electromagnetic forces with radii below $sim$50 nm are the inner source of pick-up ions. We expect the peak deposited energy flux to PSP due to dust to increase in subsequent orbits, up to 7 times that experienced during its sixth orbit.
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