It's hard to tell what's going on from this photo. The right hand part looks like it could be spray paint, in which case the question would be "why?". There also appears to be a large metal staple or something similar near the left edge of the large black area, also indicative of a problem. I'm not sure what's happening on the left hand side, the photo just isn't clear enough. In any case, this isn't normal. Being out in the sun won't turn it black, nor should it eat away at an entire layer. I can't say for sure but I think rubber roofs are white, or nearly white all the way through.
Generally a roof that's been out and unattended to will get chalky and have scattered small dark spots of mold and dirt, not large areas.
Check out this video for an idea of what "normal dirty" looks like:
It could be mold, which can be cleaned with an appropriate cleaner. Have you asked the owner what it is?
Anything is repairable but I wouldn't buy a trailer with a roof problem, especially with the roof coming loose at the edges. You just don't know how much water might have gotten in and what hidden damage there might be.