Patient Protection and Affordable Care Act (PPACA), also called Affordable Care Act (ACA) or Obamacare, requires most US citizens, permanent residents, and certain other US residents to purchase and maintain a compliant insurance plan that meets the Minimum Essential Coverage (MEC).
If a US citizen spends at least 330 full days outside the U.S. during a given calendar year, they are exempt from maintaining ACA compliant health insurance. Otherwise, they are required to maintain the ACA compliant insurance or pay a penalty while filing tax return.
Under the short coverage gap exemption, if you are not covered under ACA compliant insurance for less than 3 months in a year, you may qualify for the exemption. Otherwise, the penalty is 1/12 for every month you are not covered.
Short term insurance plans, travel insurance plans or even expatriate health insurance plans are not ACA compliant; therefore, they do not count towards maintaining Minimum Essential Coverage.
The situation can be frustrating to US citizens who live abroad for more than 3 months but less than 330 days. They are required to have Obamacare compliant medical insurance, which is most likely not going to cover them abroad or even provide a limited coverage. The penalty amount varies depending upon the income of the taxpayer; for most people it would be easier to just go ahead and pay the penalty, which is few hundred dollars, significantly cheaper than buying the lowest cost bronze level health insurance.
Of course, while they are abroad, they should be covered under expatriate health insurance.
When they are visiting the USA temporarily, they can purchase short term travel insurance. If you are already covered under expatriate health insurance with worldwide health coverage, you don't need to purchase any travel insurance.
If they are going to be moving back to the US permanently, they can try to enroll into Obamacare using a special enrollment period. If that does not work out, then purchase domestic short term medical insurance until they can enroll into ACA compliant medical plan.