Discovered these today in a far corner of our yard. Most of the fruits seem to be overripe and are falling from the tree. Also, the tree's leaves seem to have been heavily damaged by something. We live in Georgia if that helps at all.
@TheGoddessEris welcome to GS and also thank you for adding the pictures as it helps members to help you..sorry but i don't have any fruit trees but this link may help you https://www.gardeningknowhow.com/edible/fruits/peach/bacterial-spot-on-peach-trees.htm
I looks like a persimmon tree/fruit. Possoms like to eat them. I wonder if they come to your tree to eat during the night..
I think you are correct Sjoerd, it does look like persimmon. GoddessEris contact your local County Extension office, they (and there are several in Georgia do a Google search for them to find the office in your county.) are connected to the University of Georgia and have all sorts of experts who can identify the problem with your tree.
Addendum: Oh, I forgot to say that I think of blight when I see your foto of the leaves. I don't know if it exists in persimmons...but I wonder.
I was thinking it was a persimon, the fruit just didn't look fleshy enough. But I guess that makes sense if the tree is sick. The house was built in 1972, so the tree might have been here about that long. I think it was being used as a rental before we bought it, so I don't expect the tree has been cared for at all for a long time. Thanks for the help! I will be sure to get into contact with someone about it soon
Native persimmons are falling now ! They are very sweet. If you have had a lot of rain that may be the problem with the tree. But the fruit is still fine to eat ! But do not pick them off the tree unless they are very soft,, too firm fruit will sure give you pucker power !