Never seen it. But I gotta say that almost every brand of fine tuner works with either loop or ball/ring end strings.
Take a closer look, Ed. I don't see any way a ball end would work.
That looks like an old timer and probably quite precise and likely pretty heavy. I've never seen one like that, but quite a few types show up in old cases. There are a range of styles available today though.
Doug, yeah you're right. I probably just misunderstood the intent of the post. I was assuming that Johnny Mariachi was hoping to buy a new fine tuner, or maybe a set of them, and wanted to know the buying landscape. In any case, Johnny -- fine tuners are easy to install and won't be a bank breaker. In the world of fiddling, it's one of the least of your worries.
I don't know of a name, but I have a few similar but not exactly the same. They are pretty old and may go back to days before ball-end strings were common.
'5-strings' 11 hrs
'Squeaks and scratches' 2 days
'Pre WW2 Fiddle' 2 days
'Flash jams?' 2 days