The close orbit makes that less likely, due to the way orbits work. Even if the planet was moving very slowly when it encountered the star, it accelerates as it gets closer and would end up with an elliptical orbit with a farthest point at about the same distance away as when the star first became a dominant force on it. If it were our system, the planet would spend most of its time in the Ort Cloud and occasionally it might venture into the area the gas giants live in or maybe even the inner solar system. It wouldn't necessarily be on the same plane as the other planets, too.

In order to find a close orbit and stay in it, it would have to kick other planets out, giving its momentum away when it was close (which makes it rarer than just a capture, especially considering it might not even be on the same plane as other planets in orbit). Or some other event would need to perturb the orbit just right.

But unlikely doesn't mean impossible.