1a) I ate my food and you ate your food. 1b) I ate my food and you ate yours. 
2a) I ate my food and the cat ate its food. 2b) I ate my food and the cat ate its.

No-one ever specifically tells native-speaker children that sentences like 1a) and 2a) are correct but awkward, that sentences like 1b) are correct and natural and that sentences like 2b) are impossible. (I figured this out myself when creating grammar summary sheets.) Why is 2b) impossible? Your food and yours, our food and ours, her food and hers and even his food and his are all interchangeable here, but its food and its aren’t. It isn’t simply that native-speaker children never encounter sentences like this. Native-speaker children are capable of making an almost infinite number of sentences they have never encountered (and most delight in doing so).

Quite recently I actually encountered a sentence like 2b) in a published novel by an established author. Unfortunately, I didn’t note the page, so I’ll have to re-read or at least skim the part that I’ve read in order to find it.