An independent nursing consultant can be many things to many people. I mostly consult to the legal world on nursing and medical matters, doing chart reviews to help attorneys understand what they say and mean, serving as an expert witness on nursing standards of care if they are applicable in a case, and preparing and critiquing life care plans. These folks want nursing expertise and sometimes are astonished to hear what we come up with. I could tell you stories of cases that were thought to be open-and-shut and turned out to be something entirely different (usually much bigger) once a nurse got into the records and read them ... I also know how to look up the applicable resources (like Medicare rules for patient safety), actual costs of goods and services, and so forth; sometimes it's even important to know they exist.
You would have to have a very solid and extensive nursing background to do this sort of work-- it's totally not something I could have done as a fresh-faced mid-twenty-something, or even a thirty-something. Now, though, with mumblemumble years since I graduated from college I have done a lot and seen a lot more. So it's understandable that I can be of use to someone who really needs clarity on the issues to make decisions, whether it's how to proceed in a legal case (plaintiff or defense) or how to plan to make the money last in a trust case.
If this looks like something you want to think about when you have some gray hair, look up certified nurse life care planning (CNLCP), legal nurse consulting (LNCC), and insurance case management.