Is it permissible to use a bile salt supplement extracted from foreign goats and cattle, given the uncertainty regarding their method of slaughter?

If goats or cattle are slaughtered Islamically, there is no issue in the permissibility of utilizing their bile. However, if it is taken from a dead animal, it does not take the ruling of its meat in terms of impurity and prohibition, because it is not a part of it, but rather it is considered something separated. It resembles milk and rennet from a dead animal, regarding which scholars have differed in their rulings. Abu Hanifa, and a narration from Ahmad which Sheikh Al-Islam Ibn Taymiyyah chose, held that the rennet of a dead animal is permissible, pure, and does not become impure by the death of the animal. Sheikh Al-Islam supported this by stating that the Companions ate cheese made by the Majus, and that rennet and milk do not die, but rather the impurity came from them being in an impure container, yet internal contact has no ruling. Based on this, there is no harm in consuming bile salts, whether their source is doubted or it is known that they are from a dead animal.