I have not researched this in depth (and am willing to be corrected if wrong), but dead (uncontrolled) satellites and other debris are effectively abandoned and space belongs to no person or nation. So, it seems to parallel salvage of an abandoned vessel on the high seas. If the abandoned satellite/debris can be identified, the owner can be contacted to see if they want to recover custody (and pay the necessary costs for doing so). If they renounce title, then the salvor is free to do what they want with it. Since these objects are derelict, there is probably no effective way to recover them (by either the owner or salvor) and the proper course of action is to remove the hazard.
This is actually a tremendous business opportunity . Once the technology is worked out, new satellites will probably be required to incorporate a deorbit technology or account for removal as part of program costs. Eventually, some sort of probably UN-coordinated effort will be developed to clear Earth’s orbit of such materials. Spacefaring countries and companies will pay into a common fund and the work will be bid out to companies who have the technology to perform the work.
I don’t know its name, but there was a Japanese anime series based on this concept (contracted removal of space debis from Earth orbit) some years ago. Guess this is the start of the real world follow-up.