If he's replacing the box with the same model, and it's not a warranty replacement, he could do a drive swap. Then use the commonly available instructions to add (AKA "marry") the new drive to the old one, and have double the storage.
If this isn't the case, try searching the web for "Tivo" and "video extraction". A lot of the stuff that comes up looks pretty involved to me--there seems to be a lot of steps. I'm sure it can be done, but ultimately, it might be decided that it's not worth the time and effort to learn how and get it done.