What is the meaning of "sharp edges" and to be "loved off"?

I just came across the fragment below, taken from "The Velveteen Rabbit", and there are a couple of things I'm not sure I understand. What is meant by "sharp edges" and to be "loved off"?

Your help would be greatly appreciated!

You become. It takes a long time. That’s why it doesn’t happen often to people who break easily, or have sharp edges, or who have to be carefully kept. Generally, by the time you are Real, most of your hair has been loved off, and your eyes drop out and you get loose in your joints and very shabby. But these things don’t matter at all, because once you are Real you can’t be ugly, except to people who don’t understand.

Solution 1:

The story is about a toy rabbit who’s carried around and cuddled by a small child. In this passage, “people” means children’s toys. (The book is one of the inspirations, directly or indirectly, for Toy Story.)

“Sharp edges” is meant literally: little children don’t cuddle toys with sharp edges or take them to bed, because they’d get cut. And toys that break easily don’t last long enough to be some child’s beloved favorite toy.

“Loved off,” here, means that that part of the toy has worn off or fallen off from age and rough play. The unusual word choice means that the child played with the toy so much and for so long because she (or he, in this case) loved it so much. That’s not a meaning of “loved” that you’ll find in the dictionary, and maybe not even in any other book. But we can figure out from context that it means something like “lovingly worn off.”