I say, with Allah's guidance: If a chicken, a cat, or something similar dies in the well, then it is considered: If the object in the well has bloated, all the water of the well must be drawn out. If it has not bloated, then it is obligatory to draw out 40 buckets and recommended to draw out up to 60 buckets, after removing the object from the well. See: Al-Bahr 1: 124, Al-Bada'i' 1: 86, and Allah knows best.