It it not at all possible for an interstellar object to be captured into a stable solar orbit?
Stars tend to get torn apart, go into the accretion disk, and then eventually fall in. But we don't have a big black hole in the solar system.
Orbits are time-symmetric, so an interstellar object being captured into a stable elliptical orbit would be equivalent to an object in a stable elliptical orbit escaping the Solar System (again, ignoring other influences).