What if the dying drives volume won mount?
More often than not, you’re completely out of luck. I provided tech support at a University many years ago and had the opportunity to witness many failed drives. Occasionally we were able to revive a hard drive for small amounts of time by letting the drive cool down (somewhere cool and dry, not cold) and then powering it up attached to a service workstation (e.g. don’t attempt to boot from it, you may not have enough time). When a drive doesn’t mount, it typically goes to the recycle center or to DriveSavers if the data is worth the recovery cost. If you’re reading this paragraph now because you’re in this situation, my heart goes out to you.