Yes, the software can open damaged ISO files, but it can open them up to a point where the important headers are still in the right place. For example, UltraISO will open the image file but it won't allow copying for all the files contained in the package. Try extracting only the files that are still healthy and then you can rip them using another software to another format.
UltraISO features a function called Super Restore. This allows you to take advantage of the repair headers that are automatically added when the image was previously created. With a bit of luck you could turn the ISO file 100 % complete allowing you to extract it without problems.