Ol BW: that "fencerow peach" may or may not be worth the effort to care for. Give it a little fertilize this fall, clear out any brush from around it and see what happens; won't hurt to try. There are several so-called "native" peaches which can be planted now for SHTF and will likely be around in the future.
The best one for this area (Zone
is generally called "Indian Blood"; it produces late and has a purplish blush to the meat. The ones I have grown, generally grow as a bunch of sprouts rather than a single trunk. It's better for sweet-pickling, but is edible.
Another has white flesh, is rather "mealy" in texture, and grows more as a tree. If it has a name, I've forgotten it.
The best thing about them is that they will regrow from the roots when killed by borers and disease. Sometimes they have been used as rootstock for grafted varieties and come up after the grafted part dies; sometimes they come up from peachseed in discarded or fallen fruit. I've seen the Indian Blood in some nurseries. A plant called either Pluot or Plumcot is also used as rootstock and it is hardy, but makes less fruit than my cultivar trees. It, too, regrows when killed back
Another long-lived tree that I find occasionally around old homesteads is the quince (the tree, not the flowering shrub). It was generally used for jams and jellies, as the fruit is only marginally edible when raw.
My brother has planted several apple trees around his deer stands; these came up from seed in his scrap pile, and they seem pretty hardy, but the fruit is rather nondescript. I've read that most of the seed strewn by Johnny Appleseed was from cider houses and many of them developed great apples just by sheer chance.
I have two apple trees, an Anna and a Golden Dorsett (pollinators) that are maybe 12 years old and thrive, untended, except for occasional pruning back broken limbs. They give me several bushels each, each year.