Aww, that's a hard one. I definitely see your point, and understand that you really want to protect the poor thing. It is commendable that you are softhearted enough to want to look out for her. I think in your heart though, you know she isn't yours to take, or you wouldn't be asking the question. However if the hen is always on that property, and knowing that it is your parents property makes a big difference... I guess it depends on the livestock laws in your area (I am sure you could find out with a phone call or two). I know here in Ohio, if someone isn't caring for their property and you start cutting the grass and caring for it, after so long you can take ownership of the land (of course it has to be taken to court to make it legally yours); so I wonder if there is some law that of you feed/protect an animal (it is foraging and nesting in the cover of your parents property) that would allow them to take ownership and they can give it to you, but again it would probably have to be done pursued legally, IF there is such a law, so that you (or your parents) can't be sued or prosecuted for stealing it.
Either way, I agree with ChicksinPR, if the owner cares so little about offering protection and the hen is never in their yard anyway, they may not care about it at all and may just give you permission to take it, or at least allow her to brood in your coop and have the eggs after. I can't imagine that if they care so little that they actually want more chicks. It can't hurt to ask for that poor hen's sake. I can't imagine sitting so vulnerable in the long hours of the night while I was with child!
If you pursue either option (checking on the laws or asking the neighbor), I would love to know what happens, please keep us updated! :)