It is well known that planetary collisions can create moons orbiting the result of the merger if they happen in the correct way, and this is how the Earth's moon is believed to have been formed. See the animations on this Durham University page to get an idea of how the mechanism works http://icc.dur.ac.uk/giant_impacts/.
It seems to me that it should be at least theoretically possible for the same process to happen when neutron stars collide, which would produce bizarre extremely-high-metallicity (or rather high-average-atomic-mass) planets. However, I also know that the physics is very different in some ways: the colliding objects are much denser; the collision is much higher-energy; radioactive decay creates a burst of extra energy from any matter thrown off the objects; the gravity and velocity are high enough that relativity matters a lot; they probably are in very circular orbits spiraling toward each other rather than hitting each other from the angles that protoplanets do; etc.
It's also possible that most of the mass of the neutron star might be thrown away and leave a low-mass remnant that might expand into an high-atomic-weight planet or white-dwarf, or that some bit of ejected matter might be thrown out at similar enough velocities (speed AND direction) to eventually coalesce into a rogue planet.
I'm just wondering whether anyone has looked into this before, or if anyone has any input as to whether this would be more or less likely than moons forming from planetary collisions, or if anyone knows how to test this with simulations.
EDIT: I've just realized the reason why it is probably impossible for a planet to form in the same way the Moon formed around the Earth: The outward force is way stronger than gravity except for close objects, which would be inside the Roche limit of the resultant black-hole or neutron-star and thus form an accretion disc or ring rather than a planet (due to the fact that any potential planet would be ripped apart by tidal forces). I haven't done any math on this, and this is just my impression, though. In addition, this doesn't mean a planet couldn't form from the ejecta in other ways; for instance, the disc of matter close enough to be held in orbit after the initial explosion might be pushed out to include a planet-forming region outside the Roche limit during a later phase of the event.
EDIT 2: I've had an idea for how this might happen, but I think this might really be a different question. The idea is that, if another star was in the same system as a kilonova (collision between stellar remnants that ejects matter and radiation), the kilonova might leave enough of the star to stay in the system, or perhaps leave enough matter for the other star to capture it somehow. One thing about this scenario, though, is that the idea of another star being in the same system as a compact binary merger rather implies that this third star has already been hit by at least one supernova, possibly multiple and maybe several novae, depending on whether a parasitic binary was formed. (This wouldn't apply if the third star was captured into the system after both of the other stars had already died, though.) Supernovae are stronger than kilonovae in terms of energy that gets thrown out, so the previous supernovae would already have had a stronger affect on the object. I believe that kilonovae are thought to produce heavier elements than any type of supernova, so stars hit by kilonovae would be different in composition than ones hit by supernovae, but it's still basically the same question: What kind of remnants can survive from stars hit by supernovae/kilonovae/novae at close range. I think it's pretty obvious that this could form some kind of remnant, possibly depending on the distance to the third star, so that already answers my question, though I don't know what compositions are possible or what masses are likely, but I think this is really a different question that should probably be asked separately if I or anyone else want it answered on Stack Exchange.