Upgrading Kubuntu through LiveCD after Crash

I have accidentally purged some important stuff, I think, causing my Kubuntu 14.04 to not boot past the startup logo (see my earlier question on Unix Stackexchange here). I can, however, run Kubuntu from my live USB.

After I have exhausted all options that I understand, is it possible to simply upgrade my system through the live USB to 15.10 to reinstall any system files that got purged?

Where does the upgrader place the new files without me explicitly giving it permission to access my system?

My understanding of live USB's is limited, so I guess my more general question is: Do any changes happening through the Live USB are ACTUAL changes on my system, too?

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