I have two female cats, one of whom gave birth about a month ago. She made a nest in a cardboard box, and the kittens have lived there since they were born. Yet recently, the non-pregnant cat (unspayed) has taken to nursing the kittens, licking them and even growling/hissing when I approach the kittens. The mother can't even get into the box, so the kittens have to climb out to feed. Is this normal behavior?
This is not common but normal. The mothers who lost their litter are especially prone to this condition, but it can be seen with any female cat.
Most animals have a more simplistic understanding of the maternal bound. In River of Eden, Dawkins describes that female turkeys nurse anything that has some redness and makes sound like a turkey chick, whether she laid the egg that developed into that chick, even whether that is a chick.
Similarly, female cats are triggered by crying kittens. All females that I have tested this with, regardless of being spayed or not, responds to crying kittens. This is a method I use to find female cats that hide in the house or in the garden. This trigger can also kick the maternal instincts in, making females want to nurse the kittens. The females who lost their litter are already flushed with hormones so their maternal instincts kick in very fast at the slightest trigger.
Unfortunately, this behaviour can cause harm to the kittens, especially if the female is not producing milk. I know that some stray kittens died because of this.
One solution that comes to mind would be spaying the female if you already plan to do that at one point. Spaying should reduce the maternal hormone levels in time. Consult a vet before going through this irreversible process. You can also try giving the non-pregnant cat some toys that produce crying kitten sounds. (Just shove an old mp3 player into a small plush cat.) I am not sure how she will react to this, but it can't hurt. Otherwise, you can think of limiting access to the kittens.