If I stop working in one member state and find employment in another, what happens to my social security rights?

If you stop working in one member state in order to carry out an occupational activity in another member state, you will become subject to the legislation of the "new" country of employment.

Consequently, you will stop building up rights in the "old" country and start acquiring them in the "new" country. It does not matter whether or not you take up residence in the "new" country of employment. Even as a frontier worker who remains a resident of the "old" country of employment, you will be insured under the legislation of the country where you work.