I'm just wondering if anyone has ever heard of running a "f/s" bike that isnt really a full suspension, in that it has a rigid front fork. I know it seems highly impractical, but people do weird things.

No.

are you talking about a bike that is considered a softtail, but not a f/s bike? they don't make em anymore but I've seen em before.

they made those way back in the beginning of suspension.. like the mid-late 80's, before there really were suspension forks, but no modern bikes have that setup.

That's not what he meant but they do in fact make softtails still

https://www.moots.com/bike-mtn-ybb.php

Why would they make a soft-tail with no front suspension, that seems really stupid to me, what gains would that offer? Convert, what did you send a picture of? Where is the suspension, i think i may be confused on the definition of a soft tail. I had meant are there any bikes with a rear shock with a non-suspension front fork.

One of the pioneers of full-suspension bikes, Offroad who later became Pro-Flex who later were purchased by K2, first marketted their early bikes with just their Flexstem and a rigid fork. The rear suspension duty was handled by elastomers and offered just around an inch worth of travel. So I'm not sure if this fits into what you're thinking of and while the bike technically did have front suspension, it also had a rigid fork.