If you receive a pension from Switzerland and travel around the world, your insurance obligation in Switzerland generally remains in place as long as you do not establish a new residence abroad.
Compulsory insurance in Switzerland is linked to the legal domicile of the person concerned. As long as the person do not establish a domicile abroad, they remain essentially subject to insurance obligations in Switzerland.
According to Art. 23 ZGB the domicile of a person is in which they reside with the intention of settling. However, according to Art. 24 ZGB this remains in effect until the person establishes a new place of domicile. This also applies if the person embarks on a long-term trip abroad or around the world.
No, merely notifying the communal authority of one’s departure is not in itself sufficient to terminate one’s residence in Switzerland.
There is no way to be exempt from compulsory insurance under the KVG. This also applies if you have private insurance for your stay abroad.
For further specific questions concerning your personal situation, please contact your health insurer (basic insurance) directly.