How to manage to read files unreadable due to bad sectors?

ddrescue (gddrescue package, man page)

Supposing the drive has a healthy partition table, you could easily do this:

1. Create an image file of the failing drive's partition(s) onto some healthy drive (I don't want to make this harder for you than necessary, that is why we are not creating the whole drive's image, but if the partition table proves to be broken, you would have to in the end).

2. Investigate the log file (it is actually called a map file, but that is of little importance now for you), depending on the number of errors there act accordingly.

3. That means, either try to mount the image file of the partition in question directly, or run for instance testdisk on a whole disk image file, in case the partition table would be damaged, that's a perfect utility for a partition recovery, but let's start with creating the image file of the partition.

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sudo ddrescue --idirect --retry-passes=3 /dev/sdx9 recovery.img recovery.log

Assuming:

• the drives name is /dev/sdx

• the partition you need to recover has number 9

• you want to retry bad sectors 3 times

• you want to save the image file into the current directory (.)

• you want to save the image file as recovery.img

• you want to save the log file, which is very important !, as recovery.log

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If all goes well, then simply mount the image file afterwards:

sudo mount recovery.img /mnt/whateverMountPoint

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If, for any reason, the drive stops responding, or whatever error occurs, I usually just reboot the machine, and run the very same command, which will restart the process from the point where it previously stopped.

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BEWARE:

I did not realize you mentioned mounted filesystem. Which could be a problem.

You see, you should not create an image of a mounted filesystem. Instead I suggest you create some Linux USB, boot it, and then proceed with what I said.