Ok, IANAL of course but here’s how I see the situation.
You’re stuck on an island. You can hunt with relative ease, for her it’s more difficult. Unless you give her food she will starve. You will only give her food if she sleeps with you.
So remove you from the picture. If you weren’t there at all, she would starve. Nobody’s fault but hers.
So why should that be different if you WERE there? If I have money, my neighbor doesn’t, and he’s gonna starve, does that mean I HAVE to buy him food? We’re both still on an island, just a rather larger one.
Far as I know, there is no law that says you HAVE to help someone else find food. If there were, would we have so many starving people? Is it actually a CRIME to drive past a ‘will work for food’ sign-holder without giving them food? I really, really doubt it.
Of course you’re not going to help her just out of the kindness of your heart; I presume you’re an American. q;}
If you were to actively PREVENT her from hunting/gathering/whatever, that would be ‘illegal’. But doing nothing whatsoever to help shouldn’t be.
Now, she has to make a choice… does she willingly starve to death, or does she offer sex in exchange for food?
Seems to me that SHE is the one breaking the law, if anybody could be said to do so in this kind of situation. You offer a reasonably legal commodity in trade… she offers something commonly considered illegal to sell.
Now for a dose of realism… if you’re on a deserted island, presumably you’re in international waters. If so, there IS NO LAW. Go for it. And besides, I doubt anybody would really prosecute you for anything you did while struggling to survive on a desert island. “Welcome back to civilization. Here’s your cell for the next 20 years.” Why bother resucing me in the first place, dammit!!