It kind of depends on what you mean by long distance research. I know of someone who found a research project that they wanted to do at an outside institution, set up the project and is now spending a few months at that institution to complete the project. But they are on site. If you mean remotely completing research, that is a bit harder, but not entirely impossible.
If you found something like a retrospective chart review, you could probably hop on it if you got security clearance, were able to get remote access to the hospital computer system and of course the institution's IRB doesn't have a problem with you being part of the study. This however, is entirely institution dependent as far as remote access goes. The big stumbling block would be finding someone with a project at an outside institution that would want someone they can't meet with face to face helping them with a project.
So impossible no, very difficult, most likely. But hey, its worth a shot right?

Hey, Thanks so much for the reply. I will definitely try to contact someone at another institution and see if they are interested.