You don't need complex reverse slingshot interactions. You just need a low enough relative velocity to not shoot off the other side.
I would expect this to be the norm for capture, not some exotic phenomenon.
A ball doesn't need to lose energy to be captured in a valley either.
You just apply a radial force to turn a line into a circle.
Anything that approaches the sun slower than escape velocity will be captured.
You could think of it as speeding up as it falls toward the sun, it then slows down by the exact same amount as it leaves the Sun.
In order to stay near the sun it needs to lose some of that speed, and given that momentum is conserved, the only possible way is to either hit the Sun or send that momentum to a third object.
