Our Sun is moving in a prograde orbit around the galactic center with a distance of about 8 kpc. This paper says there are many retrograde stars in the galactic halo 10-20 kpc from the galactic center. Do any of these retrograde stars have an extremely eccentric orbit that would cause them to pass closer to the galactic center than our Sun?
There's a whole stream of them: https://iopscience.iop.org/article/10.3847/1538-4357/aadba3
Named Phlegethon, this is a stellar stream that covers about 75⁰ of the sky, and is probably the remnants of a disrupted globular cluster.
It orbits the galaxy retrograde on orbits that take it between 4.9 and 19.8 kpc from the galactic centre. The orbits are highly non-Keplarian. The image shows the orbits with the sun marked as a yellow dot.
Other streams exist and may have similar shaped orbits.