I haven't bow hunted in almost 20 years. To me, if it's a hoyt Carbon matrix, no cracks, yes it's worth $50. Pull it to full extension and feel for any jerk or popping in the body of the bow. If it's smooth, chances are there's no internal crack.
For $50 I'd play with it. Got one a few years ago for a couple hundred rounds of M855, probably more than $50 now, but not so much then. You do have to adjust the draw length of a compound bow to yourself. That "test matrix" thing doesn't mean anything to me either.
If you want a bow for hunting, there are a lot of affordable used bows just a couple years old on the market. I wouldn't waste time with it. Probably clunky as Hell. If I buy an old bow, it's a recurve.
Thinking about it, this would be a decent bow to play with. I'd shoot her a $25 offer maybe come up to $35, point out that it's missing the stabilizer, and only if the strings are good. In all honesty you should be able to get $50 back out of it if it doesn't suit you.
If nothing else, that would be a cool looking wall-hanger. lol
Top Manufacturers-(No particular order)
-Hoyt
-Elite
-PSE
-Bear
-Matthews
-Bowtech
Do a little research, and if you can, go to a local archery shop and shoot some bows off the rack. Most archery shops have a pre-owned section, I have seen some great deals on those racks.