It is rare (not impossible) for a predator to leave behind the kill. Cats do that, because they do not kill for hunger.

But to know for sure is difficult.

Rabbits have an enormously high mortality rate.

a head missing sounds very much like a cat, when they don't eat the whole thing...which they often do.

Argh, not sure how I forgot about cats but sure enough I chased a &^%* stray out of the yard a few days ago. Earlier this spring we found a disturbed song sparrow nest, same circumstances w/the babies on the ground, one partially eaten. I kept wondering why a predator would go to the trouble and then leave them. We've worked hard to attract wildlife to our suburban backyard and although there are disappointments at times (as to be expected) the good definitely outweighs the bad and makes it all worthwhile. Thank you all for your input!

House cats are not considered part of the ecosystem predators like hawks and foxes because they are an introduced species. prey animals have not evolved defenses agains cats, and so cats decimate local wildlife.

It is difficult when strays and people's roaming pets do this to the wildlife in your backyard. I'm sorry. If you feed the birds and there are roaming cats, you might consider not feeding the birds. It attracts them and makes them vulnerable to all predators.

Good luck.