However it’s pretty unlikely that they would strip EU citizenship from several million citizens.
No different that stripping several million people of British citizenship, no?
Also, if Scotland suddenly gets kicked out of the EU, why should the rest of the UK automatically stay in?
The rest of the UK is not the part becoming independent, and is not the part that would have to renegotiate. I think the term is “continuing state”.
There seems to be bafflingly little certainty around this seeing as it’s possibly going to be the most important issue for a newly independent Scotland. A bit of googling found this, which is as clear as mud:
http://www.bbc.co.uk/news/uk-scotland-scotland-politics-21601242
However, the EU president’s ‘hypothetical’ comments make it pretty clear that there would be no free ride. Scotland’s response is downright worrying – hoping for common sense to prevail!
Also, it’s not that unique a situation – take a look at the Basque country. I suspect that at least Spain would be pretty wary about Scottish independence and admission to the EU setting a precedent.