I'm stupid and lazy
How can it continue to work once the program itself is removed from the computer?
(I mean of course it can't store anything anymore, but I figured it'd crash)
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Every program run on Windows is to some extent loaded into and run from RAM, not directly from the hard drive. Many programs still need access to files for certain functionality, and I assume Firefox does too but you just didn't try using any functionality that did.
Obviously, this isn't the way you should be doing it, as you will break the portability of the app and lose data in the process, as well as the possibility of just completely corrupting the app so it will never work again.