Back when I had a small car and hunted from it one was a hatch back with a rack. I just hung stuff on the back of the car tied to the rack. Another car had a trunk so I just strapped them on the trunk and tied through the windows. Obviously I am not very PC and don’t care what anyone thinks about a dead animal in view. But, that was years ago also.
Now I do hunt every once in a while with the Vibe. The deck, back of seats and sides of interior are almost all hard plastic. I just slip a jet sled in on some rubber back carpet scraps with one seat down. I put gear in the sled for easy acces, but can toss a deer in it if needed. That carries a dear easy with no contact with the interior and the sled holds all the liquid and ice if needed. Given the time, I will just drive home and get a truck or get a friend with a truck, but it can be done when needed. I will not just toss a critter in my vehicle in a tarp. It would just be too big a mess if things went wrong. I would much rather get it quartered in the field and in a cooler if I couldn’t do the sled thing.
If I didn’t have a truck, I wouldn’t have anything but a hatch back I can put the sled or other large container in. They are the only way to go if you don’t have a truck rater you are hunting or anything else where you need flexible storage.
I also think a small trailer and / or a hitch hall are just too handy not to have regardless of what you have for a vehicle. The smaller the vehicle the more you really need one or both of them for hunting and all kinds of other stuff. Most people could easily do without a truck with the extra capacity of a small trailer.
One last option is one I saw a couple years ago. Late season with a lot of fresh snow on the ground and roads one day I saw a guy tie a deer to his bumper and just drag it home. No ideas how far he went, but it was a couple miles at least. Nothing closer than that the way he went for the farm I was hunting.