Yes—sometimes you can improve legibility with strong local-contrast and noise-reduction processing, though results depend on how much real detail is present in the file. A useful approach is to emphasize the scale of the lettering while suppressing both broad stone shading and fine noise.

A typical workflow is:

1. Apply a high-pass style adjustment to reduce large-scale contrast from the stone surface.
2. Reduce noise, especially color noise, so random texture and artifacts don’t compete with the carved letters.
3. Increase contrast/sharpness selectively to the remaining medium-scale detail, where the inscription edges should be.
4. If needed, do this on separate layers so you can fine-tune the effect.

This can be pushed quite far if the stone itself is unimportant and readability is the only goal.

Beyond standard photo editors, forensic or analytical image-processing tools may help. One answer specifically suggested Project Vega, which is designed more for image analysis than retouching and can be useful for edge recognition and enhancement.

If the letters were not captured clearly in the original image, no edit will fully recover missing detail—but noise reduction plus contrast enhancement is the most promising route.