Which type of responsibility relates to a formal assignment of property responsibility to soldiers within the supply chain that have the property within their custody but not necessarily for their use?

The answer is Custodial Responsibility.  This type of responsibility normally relates to Supply Sergeants, Supply Clerks and Warehouse Personnel.  It usually concerns the Army equipment in storage, either for the future to be issued or waiting to be repaired or to be turned in.  Even though you haven’t signed for the equipment face-to-face, you are responsible for safeguarding it and can be held responsible for it. If you supervise people in this capacity, you are also responsible for what they do.