The formation of giant planets such as Saturn and Jupiter would have flung debris outwards towards interstellar space; but the gravitational perturbations of passing stars would have pushed them back into the Sun's gravitational influence, so that they end up forming the inner Oort Cloud.
We tend to think of the Oort Cloud as just sort of hanging about, not doing much of anything, really, but when Batygin and Brown ran a whole bunch of new simulations, taking these physics into account, they found that objects in the inner region of the Oort Cloud may indeed move about a bit."Due to the long-term gravitational pull of Planet Nine's orbit, inner Oort Cloud objects evolve on billion-year timescales, slowly getting re-injected into the outer solar system?We have simulated this process, accounting for perturbations from the canonical giant planets, Planet Nine, passing stars, as well as the galactic tide, and have found that these re-injected inner Oort Cloud objects can readily mix in with the census of distant Kuiper belt objects, and even exhibit orbital clustering.".
We won't know exactly how eccentric that orbit might be until more study can be conducted of the clustered objects, to determine which of them originated in the inner Oort Cloud; but, there's a limit to how eccentric the orbit can become before it is no longer consistent with our observations of the outer Solar System.