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I managed a CentOS system where someone accidentally deleted everything from /usr, so no lib64, and no bin. I didn't have a way to get proper files at the time, so I hooked the drive up to my Arch system, made sure glibc matched, and copied yum and other tools from Arch.
Booted the system, reinstalled a whole lot of yum packages, and... the thing still worked.
That's almost equivalent to a reinstall, though. As a broke college student, I had a laptop with a loose drive, that would fall out very easily. I set it up to load a few crucial things into a ramdisk at boot, so that I could browse the web and take notes even if the drive was disconnected, and it would still load images and things. I could pull the cover off and push the drive back in place to save files, but doing that every time I had class got really tiring, so I wanted it to run a little like a live system.
I have taken a drive with filesystem issues, mounted on a different machine and either backup data I wanted to keep or copy files to make the original machine runnable.