What is the ruling on praying on a prayer rug whose place or material of manufacture is unknown, and is it permissible to pray on it if there is a probability that it is made from something forbidden or impure?

It is permissible to pray on a prayer rug whose place or manufacturer of origin is unknown, for the fundamental principle regarding things is purity unless their impurity is proven. What a tailor or shoemaker produces is considered pure, whether the craftsman is a Muslim or a disbeliever, whether they pray or not, because craftsmen generally take care in their work.