There was a small snake hiding in the grass. I pointed my camera, but I zoomed too much. When I pressed the button to adjust the focus, the autofocus complained because it was out of range. I tried again, but I pressed too much and I shot a picture out of focus. Then I changed the zooming level, but in that fraction of a second, the snake and the good frame were gone. I tried to sharpen the image with Gimp unsharp mask, but it is too much out of focus. Is there another way to sharpen the image?
Yes of course it can be post processed. It might make it “better.”
But it will never make it the picture you wish it was.
The good news is that there will be other snakes on other days. Plenty of chances to make better snake pictures lie in the future if you want.
There are good reasons to work on pictures that probably can’t be saved. One is to practice using post processing tools. You will understand what is possible. And what is not. And develop intuition for what might be.
In the long run, most of the pictures we make turn out worse than we wanted. Experience teaches us that the way to get the good ones is to focus on trying to make them and not worry about the ones that got away.
The only way not to make pictures that are not good enough is to not make pictures.
Better than sharpen, you can deblur the image. You could use techniques that are not usual in consumer photography such as blind deconvolution, or patch-based techniques such as BM3D deblur which can deblur from one single image. There are other techniques.
You can use Matlab (a standard tool in computer vision) to apply those techniques (implementations of those exist), and Photoshop can use Matlab functions, which is practical for applications on images.
Example with blind deconvolution:
Example with BM3D: