Title.

I know there are tools to set up a linux distro's installer on a USB flashdrive. What I'm looking for is slightly different: I want to install a linux distro (a Debian derivative, but am still unsure which) on a USB hard drive, but I want to do it from a running system, rather that have to boot into installer mode.

The rationale is that this is the only active machine I have ATM. I guess this exists since that's how "live distros" with installers even function in the first place, but I haven't had much luck searching for information.