The first one that came to mind was fli4l (Floppy ISDN for Linux). Originally a distro of German origin that fit on a single floppy disk to turn a 386 or 486 PC into a router for ISDN connections. Last I looked it's still actively worked on.

There are probably tons of more obsuce ones. But this is one I actually used.

Suicide linux. Nobody can run it for more than a day

Edit: i just searched "suicide linux" to see if it still exists and one of the top results was ian murdock's wiki page, :(

elive

you think a distribution that automatically includes all the proprietary stuff that we use baked into the distro would be more popular since it makes linux ready to go for most people; but it still gets fewer than 300 clicks per month.

Windows 11

Rarely hear about DSL anymore, http://www.damnsmalllinux.org/

Take your pick from the Linux family tree

Well I don’t hear much about Gentoo, Damn Small, Puppy or Knoppix anymore. Wonder if they still exist.

I haven’t done much disto hopping since I settled on Ubuntu around ‘08 and then on NixOS last year. I like my systems working when I need them and waiting around for a new install to finish is boring to me.

most obscure and to me coolest but unfortunately not very active https://sourcemage.org/

Kolibri

Yellow Dog

I actually ran this on a PPC Mac back in the day

Chimera Linux

Jolicloud. I ran it on an old low-spec netbook in 2013ish, basically a ChromeOS before Chromebooks were a thing. It was discontinued in 2016 but great for the hardware while it lasted.

Linux STD! Waaaay before skiddos had backtrack or kali

Obscure as in "only for a very specific purpose and nothing else"?...

Well, there is the Mircrosoft linux distro for their azure cloud

I guess DD-WRT as distro for router is also kind of obscure. Or the more general openWRT for embedded systems.

I created a distro once for class that just had diaspora installed on a live CD. It was only used for demos a looong time ago. DiasporaTest.

The old PearOS(which looked like a meme-ish knockoff MacOS), UwUntu and Nyarch

I imagine there was a time when this wasn't obscure, but I'm guessing people today don't remember Caldera OpenLinux. That was the first Linux distro I installed/used. A guy from church gave his copy.

Caldera eventually became SCO. But I'm pretty sure I was using Caldera OpenLinux before the whole Novell patent suit thing.

Probably KaOS. It puts a strong focus on KDE and Qt.
As in, it doesn't package programs using different GUI toolkits, aside from the most popular, like Firefox and GIMP. When I tried it a few years ago, you also had to enable a separate repo to get access to these.