Megillah 13b: Haman said to Achashveirosh, “If a fly falls into a Jew’s cup of wine, he throws out the fly and drinks it, but if my lord the king touches it, he spills it on the floor and does not drink it.”
ואפילו נופל זבוב בכוסו של אחד מהן ־ זורקו ושותהו. ואם אדוני המלך נוגע בכוסו של אחד מהן ־ חובטו בקרקע ואינו שותהו.
The Chasam Sofer (Yoreh Deah 94) tells a story took place in Frankfurt: a chicken flew into a vat of boiling butter and died there. A great rabbi (the Chasam Sofer does not give his name, but some say that it was Rabbi Nosson Adler, the Chasam Sofer’s teacher) ruled that the butter was forbidden and they could not even sell it to non-Jews. So they poured it out onto the street. Afterwards, someone reminded him that the Rema says that any milk and meat mixture that is only Rabbinically forbidden to eat, such as chicken and milk, is permitted to derive benefit from, and therefore may be sold to non-Jews. He replied on the spot, “Yes, it was permitted to derive benefit from the butter, but it was forbidden to sell it to non-Jews, because it absorbed the taste of meat from a live animal.”
The Chasam Sofer comments that it was clear that Rabbi Nosson Adler’s original ruling was not because of meat from a live animal; rather, he had indeed forgotten the Rema’s rule that it is permitted to derive benefit from chicken with milk. But Hashem does not allow a tzaddik to make a mistake, and therefore the ruling turned out to be correct for a different reason. Hashem placed this quick answer in his mouth to save him from embarrassment.
We see from this story, concludes the Chasam Sofer, that live animals can give taste to a mixture. Thus the chicken, while still alive, was giving taste to the butter and forbidding it to non-Jews.
The Chasam Sofer’s student Reb Boruch brought additional proof to this from the Rosh in Avodah Zarah 68b, who cites the words of Haman – that a Jew would drink wine touched by a fly – as proof that cold things do not give taste. But maybe there the fly was alive and therefore could not give taste! From the fact that the Rosh ignores this argument, it would seem that he holds that live animals do emit taste.
However, the Amudei Ohr argues that it is unheard of that an animal or person, simply by touching a hot food, should render it forbidden. Therefore the Steipler (Chullin 5) argues that in Rabbi Nosson Adler’s case, the butter was forbidden because some part of the chicken may have become separated from the chicken while the chicken was still alive. That limb, forbidden to non-Jews, is itself dead, and therefore it can emit taste. But a completely live limb, such a human finger stuck into coffee, would not emit taste and forbid the coffee.
As to the Rosh’s comment on Haman’s words, perhaps the Rosh assumed that the fly in question was dead, but a live fly would indeed not emit taste.