Not in Newtonian gravity with particles. This situation is soluble with stable elliptical orbits, so any examples would have to depend on either Relativity, or that the bodies are not particles.
If the bodies are not rigid, then tides can cause the bodies to separate, this is happening with our moon, but in general, if one of the bodies is rotating rapidly, then tides can transfer angular momentum from the rotating body to the orbit, however as the two get further away, the tidal effect reduces. This can't cause one body to be rapidly ejected.
So looking at relativity, there is a possibility. First you need a (rapidly) rotating black hole. This has a region, called the ergosphere, from which an orbiting body can extract mass/energy from the black hole. A process to do this was described by Roger Penrose. An orbiting body must enter the ergosphere (but not fall to the event horizon), split up, with one part falling into the black hole, and the other part being pushed forward. The net result would be that the rate of rotation of the black hole would lessen, and the part of the body that didn't fall into the black hole would gain energy. Potentially it could gain a lot of energy. (more than 20% of its rest-mass energy)
This is quite an exceptional situation, and you don't get the whole body back, some must necessarily be left behind. It could be used to eject one member of a binary system
The final category in which a binary can eject a member, is when one part of the pair does something fundamentally non-gravitational such as "explode". The physical push from an asymmetric supernova can eject it from a binary system, but I don't think that this is what you quite mean.