What is the ruling of the Sharia regarding a debt resulting from theft, with current inability to repay, and inability to inform the owner of the money for fear of exposure, along with the intention to repay when able?

You have done well by repenting from theft and betrayal of trust. Part of completing repentance is returning the rights to their owners. If one is unable to return the rights to their owners, the money remains a debt upon him, which he must pay whenever he is able, or seek the owner's forgiveness. If he is unable to pay or seek forgiveness, he must resolve to return the money whenever it becomes easy for him, while making abundant supplications and seeking forgiveness for himself and for the owner of the right.