Could be the unit has failed on another level, but usually you'd see
a standard notice on the screen if or when the external drive or device
had been accidentally unplugged. The warning (when apparent) says
something to the effect 'Disk Not Properly Ejected' or 'Unmounted'
and when this happens, the content on the drive may become damaged
or unreadable by the Mac.
If the cable can be replaced (both ends with plug connection) then you
may see if exchanging the cable can help. Also restart with the hard
drive attached. Sometimes this may let Disk Utility 'see' it, if not Finder.
If you have a PC or other non-Mac system, there are a few times where
another computer may be able to see these drives; but to use them is
yet unlikely because of the format difference. You can still lose content.
There had been a few good third party disk utilities that may help
recover content, however the drive would have to be located by
the macOS or another system. Some of these utilities have a 'free
scan' to see if their software (retail purchase) could locate/recover
the content of a hard disk drive or flash drive. Then, you pay a fee
to unlock the software. I've doubted their claims, to percentages.
Companies such as ProSoft Engineering have Data Rescue software
utilities that could be useful; some versions are available on USB flash.
https://www.prosofteng.com/data-rescue-recovery-software/
Recent search of current version w/ reviews: 'data rescue 4 review'
Another name that comes up, still a retail product, is Disk Warrior.
Each of these tends to have some specific angle they do best at.
www.alsoft.com/DiskWarrior/
Others, such as 'Drive Genius' are usually for system boot drives,
so their usefulness may be limited even when used for a process
they were intended. See 'Prosoft Engineering' site details for this.
These usually only work if the drive can be detected on the bus,
or if swapped out to a known-good enclosure. Or, if you happen to
have an equivalent product to 'Universal Drive Adapter USB' from
newertech; as this example listed at otherworldcomputing online:
https://eshop.macsales.com/item/NewerTech/U3NVSPATA/
This can use a bare drive (includes its own power supply & cables)
to perform various tasks with hard drives, outside of enclosures.
Sorry to not have a 'method without instrumentality' as most these do
do require something or another - that most people may not have...
Or have and did not use, such as a method to create duplicates, &
extra drives on which to archive them, & no time before trouble set in.
Good luck in any event...! 🙂