Keratin starts out as specialized skin cells. The process of cornification is how the cells “die” and lose their metabolic and reproductive machinery, leaving behind a distorted cell structure full of rigid and flexible proteins.
And as a counterpoint, milk is initially secreted with white blood cells from the mother. Is there a meaningful distinction between “living tissue because lots of cells” and “not living tissue because few cells?” Even if you say there is, it’s still arbitrary.
Yeah, most fruit is also harvested with no harm to the plant, and with a side benefit of spreading the plant’s progeny. Granted, the process is a bit different the way we do it (we mostly deliberately cultivate the plants whose fruit we eat, instead of just pooping out the seeds), but the net effect is the same.
Ultimately, though, the question is considerably complicated by the fact that substances aren’t alive; organisms are. You can look at a plant or an animal, and break it down into a (rather long) list of all of the substances it’s made of: The water isn’t alive, and the polypeptides aren’t alive, and the polysacharides aren’t alive, and the nucleic acids aren’t alive, and the glycerides aren’t alive, and so on… but when you put them all together in the right way, the combination of all of them is alive.
Actually, milk does has living cells. A quick cite from Google, Cells of human breast milk. I assume other species’ milk has living cells as well.
Edited to add bottom line from cite: “Considering its composition, function, rich biological ingredients and cellular contents, breast milk can be considered a living tissue.”
Oh, and to add to the list, “vinegar” (or at least, a 10% solution of acetic acid, which might or might not be legal to call vinegar) can be made from petrochemicals. The petrochemicals themselves are usually derived from the remains of organisms, but there are such things as abiotic petrochemicals.
If we’re talking about salt then we should also mention baking soda, baking powder, and alum.
What may be unique about honey and milk is that they are created by the bees and mammals specifically to be used as food. I can’t think of anything else we eat where that’s true.
Milk is created by female mammals. (Some birds like pigeons and flamingos feed their young on “milk” produced in the crop.) But honey isn’t created by bees, it’s processed from nectar made by plants to attract pollinators. So if you count honey, you would also have to count fruit jam.
There’s the curious case of the Florida stone crab. The claws can be removed and the crab returned to the water where it can survive and even regrow the claws. Rather like fruit trees, part of it can be harvested and eaten while the organism survives.