Can I install a distro booted from a drive to the same drive?

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http://unix.stackexchange.com – I know how stupid this sounds BUT is it possible to install a linux distro that has been loaded to the drive it was booted from? I was thinking of installing Arch or Puppy to a flashdrive that Would be hosting itself. OR Is there a precompiled drag and drop style distro that you can drop the files to and run with constant persistence from drive to drive? Other limiting factor is that the overall size of distro must be <4GB. EDIT: To clarify, I want to install a system to a flashdrive that it is livecd'd from. Scenario for reference: I use LiLi to put ubuntu-minimal.iso on a flashdriv (HowTos)