Ddrescue
When disk fail or start failing you should back it up by making a copy of the hard drive then running the backup process.
in simple cases the dd command can be used but it will often choke on failing drives.
GNU ddrescue is a much better tool to use, it will do a very good job of getting a data off a failing disk. N.B. it can take a very long time to do so if a drive is really bad. It should not be confused with dd_rescue. Though both do a similar job GNU ddrescue is the superior tool.
to run it you need to do:
sudo ddrescue /hard/drive output.dd log.file
e.g.
sudo ddrescue /dev/sda1 99999.dd 99999.log
Use the ticket number to name the output file and log. Including the log is very important. ddresuce will run with out it but the log file enables the process to resume if it is interrupted for any reason.
Note it is possible to make a copy of the whole disc, rather than individual partitions (if for instance, there are multiple partitions to backup) but it makes it a little trickier to read the resulting image.
GNU ddrescue will work with any block device e.g. cdroms, usb thumb drives, not just hard drives.
ddrescue tries very hard to rescue the data1 and even it can't read it will rescue the remaining data in such a way as to preserve the file system structure (it leaves the unreadable parts blank but this won't affect other files).
The full manual is here: https://www.gnu.org/software/ddrescue/manual/ddrescue_manual.html
1. Rather than try to read data in a linear fashion it divides the disk up into sections. If it has trouble reading a section it divides it again, splitting it up until it finds the smallest unreadable section.