Okay...
First off, the rabbit died as soon as I opened the world. I continued killing other mobs, but didn't get the same results. 2nd, I deleted the world because after playing on it, it became 'corrupt,' where the world kept crashing after opening it to LAN (which I have reported to Mojang), the only reason to play it. And finally, to reproduce, walk up to a rabbit (or who knows, any other mob might work, and could possibly only work in the snow biome), kill said mob (maybe getting a critical to finish it off), and there's a rare chance that the game will suddenly crash. Since I'm not an expert at these things (as you can tell by my description...), that's all I know.
It seems like I'm doing everything wrong...
First, I forget to turn on VBOs. Now, I'm using an outdated version and creating an issue about it.
I found a bug almost exactly similar to this, the only difference being that no matter how far I go or how close I get to the missing chunk, it won't render. This problem happens for me with VBOs turned on and off, by the way.
EDIT
Adding on to that, whenever I press Escape and then un-pause the game, the chunk renders but now a different chunk is missing. Same issues from original post.