There was a large Ex-pat community in Spain before and will continue to be, my parents who have a house out there and been constantly hit with new taxes from the Spanish government because they were not Spanish, that would not happen over here, most notably was a change in car driving where you now have to pay some hideous fee if you intend to keep a British car in Spain, taxes on the bank accounts because they are English based...
But Spain will not suddenly tell all these Ex-Pats to GTFO, simply wont happen
I know that, I was mostly being facetious earlier, but it's not beyond the realms of possibility they'll either have to get citizenship or pay for a visa to remain. In fact as each government would have to have some way of legitimatising ex EU migrants (you know so they could enter and leave the country at some point), there's almost certainly going to have to a process other than just everything staying exactly the same.