The outer solar system exhibits an anomalous pattern of orbital clustering, characterized by an approximate alignment of the apsidal lines and angular momentum vectors of distant, long-term stable Kuiper belt objects. One explanation for this dynamical confinement is the existence of a yet-undetected planetary-mass object, “Planet Nine (P9)’’. Previous work has shown that trans-Neptunian objects, which originate within the scattered disk population of the Kuiper belt, can be corralled into orbital alignment by Planet Nine’s gravity over ~Gyr timescales, and characteristic P9 parameters have been derived by matching the properties of a synthetic Kuiper belt generated within numerical simulations to the available observational data. In this work, we show that an additional dynamical process is in play within the framework of the Planet Nine hypothesis, and demonstrate that P9-induced dynamical evolution facilitates orbital variations within the otherwise dynamically frozen inner Oort cloud. As a result of this evolution, inner Oort cloud bodies can acquire orbits characteristic of the distant scattered disk, implying that if Planet Nine exists, the observed census of long-period trans-Neptunian objects is comprised of a mixture of Oort cloud and Kuiper belt objects. Our simulations further show that although inward-injected inner Oort cloud objects exhibit P9-driven orbital confinement, the degree of clustering is weaker than that of objects originating within the Kuiper belt. Cumulatively, our results suggest that a more eccentric Planet Nine is likely necessary to explain the data than previously thought.