Along the year, we always get photos sent to us to help diagnose a problem. This photo was sent to Monte Nesbitt from Schleicher county where a homeowner was having problems with their peaches.
Our best guess (we have seen this before) is Rhizopus rot. Common bread mold can be a post-harvest pathogen or even attack fruit while it is still on the tree. There are no visible signs of sporulation yet, but within a day or two, these lesions will display a black mat of spores on the surface of the fruit. No real remedy for this other than to consume the fruit before it gets to this stage of softness.