Conclusion
Normally, Medicare only covers the cost of your healthcare services in the United States and the territories within it. When you move out of the United States, this plan becomes invalid. However, there are some instances that make insurance active outside the United States.
In the case of an emergency, if the hospital closest to you is in a foreign country, Medicare covers the cost of the emergency. The same thing happens if the only hospital closest to you that can treat your condition is a foreign hospital when you are living in the U.S.
If you plan on moving abroad, you can seek other options like a Travel Insurance plan which does not only cover the cost of your healthcare. It covers the cost of stolen items or items that might be damaged during your journey.
References
[1] https://www.medicare.gov/sign-up-change-plans/different-types-of-medicare-health-plans
[2] https://www.mayoclinic.org/diseases-conditions/end-stage-renal-disease/symptoms-causes/syc-20354532
[3] https://www.cms.gov/Medicare/Health-Plans/Medigap
[4] https://www.allianztravelinsurance.com/
[5] https://www.tricare.mil/