The business of recovering vital user data from a failed NAS (network access storage) device is best left to the experts. Unless you have skills in NAS data recovery, then your chances of successfully recovering the data are very small, however your chances of placing the data beyond the abilities of even a professional to recover the data are large.
Even assuming you can successfully remove the hard drive (or hard drives) from within the NAS enclosure you then have to clone those hard drives. More likely than not this will involve physical repair to one or more of the hard drives, for example the read/write heads may have failed and need replacing. Alternatively it may involve being able to work around a number of bad sectors which has caused the hard drive to become inaccessible.
Let us make the assumption that you are successful with obtaining the clone. You then hook that clone up to your computer and attempt to extract the data. However you see nothing, the hard drive itself is correctly identified but there is no file system. The reason for this is that the NAS file system is proprietary and requires specialist knowledge in order to achieve NAS data recovery.