A bit late to the discussion, but I thought I'd just add some pointers for future reference.
Not all Strays can be Saved?
This is an absolute truth unfortunately.
Not only is there the question of Rehabilitation which is not always possible depending on how long the cat has been feral, but Disease.
Stray Cats are more likely to contract Feline Aids, and though I do not know how prevalent this is in the USA it is a concern this side of the pond. This can result in a nasty death and it is often much more humane to put them down.
All Cats that go through peoples trash are strays?
Not So!
Some cat owners do not feed their cats enough and/or have more than one so there is competition for food. This can result in the cat getting food from where ever it can.
Un-Neutered Cats Have a wider territorial range?
True.
A male Tom cat can have a territorial range which can be as large as a small city. Un-neutered females are next with range but it will be considerably less than a Tom Cat.
Neutering your cats will stop them 'straying' to far from home and make it less likely to suffer an accident or being picked up by somebody else who thinks that they are a stray.
Cats can't survive sub zero temperatures?
Not necessarily true, it will depend partially on the genetic traits which the cat has. For example a Scottish wild cat can survive extreme cold, and they will have a spring and summer malt like a lot of furry mammals. The Scottish Wild cat is also becoming rarer because they are able to breed with domestic moggies.
There that's it for now.
Hope it goes well with your mystery kitty, but don't be too down your not the one who put the cat in the position it is and well you've done what you can.
It would be nice if every one cared as much as you obviously do!