Is a trust that was not requested considered a debt upon the one entrusted with it?

What your friend gave you is a trust (amanah), not a debt. You must safeguard it, for Allah the Almighty says: {Indeed, Allah commands you to render trusts to whom they are due}. If it perishes without your negligence or transgression, then you are not liable for compensation. If you fear death, then write a will concerning the trusts and debts that are upon you, based on the hadith: "It is not right for a Muslim who has something concerning which a will is to be made to spend two nights without having his will written down with him."