What is the ruling on killing elephants and the like to benefit from their tusks, given the resulting extinction?

The fundamental principle is that hunting is permissible unless it is for amusement and diversion. If it is for earning a living or for eating meat, there is no disagreement regarding its permissibility without any dislike. However, hunting for amusement was disliked by Malik, and he forbade it.

If hunting animals leads to their extinction and causes an ecological imbalance or misses a therapeutic benefit, then hunting them is not permissible, due to prioritizing the public interest. However, if their extinction does not entail any harm, then there is no objection to hunting them.

Scholars have differed on the purity of ivory (elephant tusk), with several opinions: impure (Hanbalis, some Shafi'is, and Hanafis), pure (Hanafis, some Shafi'is, and a narration from Ahmad), and differentiated based on whether the elephant was ritually slaughtered or not (Malikis).