Does the principal have the right to demand money from his agent who was in a car accident that caused him to lose the money? And what is the ruling if the agent lost the money without an accident?

Your trustworthy friend is not liable unless he transgresses or is negligent. If his negligence in safeguarding the trust is proven, then he is liable. Negligence concerning trusts, if it leads to their destruction or loss, necessitates liability. However, as long as the trustee does not transgress or is not negligent, he is not liable.