There is some useful information in a pdf document
entitled: "Securing Citizens’ Rights under Article 50: Reflections on Phase 1 & Considerations for Phase 2 of the negotiations" prepared by British in Europe - The Coalition of UK Citizens in Europe. There is a link to it near the bottom of page 7 of the article linked by Bob
concerning voting rights in another thread
On page 19 of the document it discusses healthcare after Brexit and refers to Regulation 1231/10
. This Regulation extends the EU’s social security coordination rules in Regulations 883/2004 and 987/2009 to third country nationals, who are legally resident in a Member State. Regulation 883/2004 is the one that provides reciprocal healthcare, pension and other social benefits between member states and Regulation 987/2009 gives implementation information for Regulation 883/2004. Effectively it means that when the UK becomes a third country after Brexit, i.e. not a member fo the EU, our healthcare and pension rights could still be protected provided the EU accepts us as living within the EU legally.
It is not completely straightforward so I would recommend reading the discussion starting on page 19 of the BiE document.