Others have been caught out, and I have little sympathy (none in fact) for them. Those who retired early to France, and other EU countries and played the system. Never de registering in the UK, and never registering in the EU - and playing both systems in fact. They have had a very hard awakening! Those people kept an adress in the UK, sometimes a family member, and would go back and forth, using whichever system suited them best at the time. Same for taxes, number plates, insurances, etc.
One thing that is clear on NHS website, is that anyone who lives abroad, with or without S1- has to de-register from their UK GP, as the NHS is resident based. For several reasons a) to free a valuable space on their list b) so they stop being paid for you being on that list c) so your notes can be forwarded to your new GP abroad.