Is a friend obligated to guarantee the money that the questioner's father gave him to trade with, knowing that the trade lost money and the partner absconded with it?

Summary:

What you mentioned about your father giving money to one of his friends to trade with, according to Islamic rules of trade (on profit and loss), is a Mudarabah contract. However, your father's condition that his friend guarantee the capital makes it invalid. If the Mudarabah is invalid, some scholars say that the owner of the capital receives the profits and the worker receives the wage of the like (Ujrat al-Mithl).

The claim by the Mudarabah worker that the money was being traded by another person makes him liable for this money if he gave it to that person without your father's permission. Therefore, you have the right to demand the original capital and the profit, if a profit was made, unless it is proven that your father had authorized this action.

And Allah knows best.