No, it isn't correct. The word 'stay' is wrong here, regardless of the form. I don't think that this was written by a native speaker. A better way of saying this would simply be: ...leaving the animals' bodies with bullets still inside.

Neither stayed nor staying are correct. We would not use the verb 'stay' here at all. Either remove the word totally, as Patrick suggests, or say 'with bullets (still) LEFT inside' (verb: to leave). Su Ki is right too - a native-speaker would not have written/said that. I hope!!!

A lot of the passages here purporting to be quotations from essays, books, textbooks and articles are written in bad or incorrect English. Some learners have consistently quoted nothing but bad English. Why is that so? Are learners hampered like me by big fingers on a small phone keyboard, and the mistakes are only typos. Or do they read a lot of rubbish material written in bad English? If so, why? There is really no need to read rubbish. There are so many good books and newspapers available.

Exactly.