What is the ruling of Islamic law regarding my responsibility for a sum of money that my relative invested in a restaurant in America through me, knowing that I was neither a guarantor nor an undertaker, and contact with the restaurant owner was lost after the events of September 11, 2001?

If the matter is as mentioned, then the questioner is neither a guarantor nor responsible for his relative's invested money. The restaurant owner is not liable for the damage of the money invested with him unless he committed transgression or negligence, because he is a trustee. The agent and the Mudarib (partner in profit-sharing) are trustees, and their claims of delivery, damage, or loss are to be accepted under oath unless they are known for treachery or negligence.

As for the agreement to deduct 5% of the net profits in exchange for covering communication expenses, it is invalid due to the presence of Jahalah (ambiguity). Rather, the actual expenses must be deducted.