Sometimes, but only partially. If the corruption is in the JPEG Huffman/bitstream data, recovery is usually very limited because that part of JPEG encoding has little redundancy. In many cases there is no software fix that can reconstruct the missing image data.

What you can try:

• Check whether the files are progressive JPEGs. If they are, you may be able to decode only the intact early scans and salvage a complete but lower-resolution version.
• Compare the damaged file sizes with similar JPEGs from the same camera/settings. A much smaller file may be truncated.
• Open the file in a hex editor: if large sections are zeros or the file was cut off, that explains grey blocks/bottom areas.
• Some corruption comes from invalid marker bytes in the JPEG bitstream; specialized JPEG repair tools may get decoding further, but they usually can’t restore the missing detail.
• For visible glitches like shifted bands or partial damage, manual retouching in an editor may be the only practical option.

So: yes, partial salvage is sometimes possible, especially with progressive JPEGs or minor structural errors, but fully recovering corrupted JPEG image data is often not possible.