Does Anyone Know...

...what happens if one of us wanted to leave the US and move to Canada or Europe or something (essentially, a country that isn't our home country). Could we just start over someplace else without any legal consequences and be able to work and eventually gain citizenship in that country? Or is this illegality going to follow us forever?

Yes you can start over without legal consequences and will be able to gain citizenship eventually. No this illegality won't follow you forever or in other countries.