As I write listening to a piece of music for piano left hand and cello (presumably both hands...), I wonder if there are any pieces of music available for stringed instruments outside the piano harpsichord harp and lyre group, that are written for left hand only. Or are these not possible, perhaps?

A violin/cello/viola etc cannot be played without a bow, which is held in the right hand.

You could lay it (violin family, guitar family) flat, and pluck the strings with your left hand - but your tune would only be able to use the four notes to which the instrument was tuned, since you cannot use the other hand on the fingerboard to change their pitch. Pretty boring! I would be surprised if anyone had put in the effort to do it.

Yes, I thought it might be too hard. However, I've just thought of one type of stringed instrument that could be played with fairly simple modification - the hurdy gurdy. https://en.wikipedia.org/wiki/Hurdy-gurdy https://en.wikipedia.org/wiki/Hurdy-gurdy

There *are* left-handed violins and left-handed violinists but they are not common; mostly because opposite-handedness can cause problems when playing in an orchestra. And an overwhelming majority of professional violinists play in an orchestra. Most violin teachers go to great lengths to force left-handed people to only learn how to play right-handed.

https://www.connollymusic.com/stringovation/left-handed-violinist-what-you-need-to-know
https://violinspiration.com/left-handed-violin/

Here is one site that lists several famous left-handed violinists.

https://www.cmuse.org/famous-left-handed-violinist/

As to any music written to be played specifically for the left hand there are examples of pizzicato music written for the strings to be plucked with the left hand. Niccolo Paganini wrote two particularly famous ones - 'Caprices' and a variation on 'God Save the King'.

Often cited as the hardest works for solo violin, Niccolò Paganini’s Caprices make up 24 fiendishly demanding pieces for the string instrument, packed with double stops, left-hand pizzicato and endless spiccato bowing. It’s no wonder people thought Paganini was in league with the devil…

In 1829, Paganini decided to compose a highly virtuosic set of variations on the theme of England’s national anthem, ‘God Save the King’, featuring his signature techniques of left-hand pizzicato and spiccato aplenty.

https://www.classicfm.com/discover-music/instruments/violin/hardest-pieces-for-violin/

However, other than 'pizzicato'or similar methods, playing a violin requires the use of both hands; one to hold the instrument and vary the pitch of its strings, the other to 'draw' the bow. While they may exist, I've been unable to find any examples of music written specifically to be played by a one-handed violinist.

Playing pizzicato requires two hands just as bowing does, unless it's a part requiring only G D A and E. If it's a whole movement, the bow remains on the music stand, but if it's an arco to pizzicato change followed by a change back to arco the bow is still held while the strings are plucked. It should be possible to equip a hurdy gurdy with a pedal to operate the turning of the wheel, and also to control the variations of speed that give rhythm, but a mechanical bow would be difficult as the violin in use moves quite a lot. Also the angle of attack is different for each string. Incidentally, the music for one handed players of the piano that I hear seems to be for left handed ones, like the one I was listening to - Nicholas McCarthy (who was born without a right hand). https://en.wikipedia.org/wiki/Nicholas_McCarthy_(pianist) The pieces for left hand are sometimes given by two handed players, who probably find the same problem that I do as a recorder player when trying to learn the tabor pipe - keeping the idle hand idle...

Here is a video of an actual one arm violinist...

https://youtu.be/DdY5FNMzq0Q

The following page gives instruction on how to play pizzicato chromatically using all violin strings with the left hand only.
only. https://www.simonfischeronline.com/uploads/5/7/7/9/57796211/076lef~1.pdf

The following YT page shows an instructor demonstrating the technique using only his left hand. https://www.youtube.com/watch?v=5VH4c0-p-CY