The issue arises when you crate a link from an individual or event listed in your database program and an external photo, document or video or audio recording. I am not aware of any of the programs that make a copy of the media item and incorporate it into the program. At best, the programs make a thumbnail or small reproduction of the item for inclusion. The program then records the path to where the actual item is stored on your computer.
I have tried to solve this issue by storing all of the images for all of my programs in one huge file folder on my computer. That way, I can link to the items in that folder and as long as I copy the folder to the new device, my problem of maintaining a link to the files is solved. In my case that file does not hold all of the media items, only those that I have already attached to one of my programs. As that file grows, I will likely have to come up with some alternative storage strategies.
What if you cannot find the photo or image of the document on your computer? I suggest downloading a copy of Google's Picasa. Once downloaded, Picasa will inventory every image on your computer. The images will not be moved and no copy is made by Google. But you will be able to use the programs editor to edit the images and move, rename and delete the images.
You may want to check the options or preferences for your genealogical database program. Usually, the programs allow you to designate the preferred folder for your documents and other media items. I always try to use one folder, as I said, for all my programs so this is pretty easy to figure out. You might become aware that almost every program has extensive instructions about what to do with broken links. Most of the online resources are program specific. So do a search for broken links and add the name of your software program.