Does Amr have the right to demand from Zayd the sum of money he gave him to invest after Zayd's bankruptcy due to the escape of his partner, and is this considered a Mudarabah or Inan company, and is Zayd obligated to return the money or part of it?

This transaction is a mudarabah (profit-sharing partnership), and the loss therein is borne by the owner of the capital. The mudarib (agent/manager) is a trustee and does not guarantee against loss unless there is an act of transgression or negligence on his part.

It is stated in Kashshaf al-Qina: "The agent is a trustee regarding the mudarabah funds... he is not liable for what is lost from the mudarabah funds without transgression or negligence."

If the mudarib is transgressive or negligent, he is liable for the principal capital; otherwise, he is not liable for anything. The determination of transgression and negligence is referred to experts.