Even foreigners can enroll in private insurance

If you are a foreigner residing in Japan and have a residence card (unless you are a Temporary Visitor), you are probably enrolled in the National Health Insurance.
The National Health Insurance covers part of the medical expenses of its members, but it does not cover living expenses during absence from work due to illness or injury.
If you are a foreigner staying in Japan with a work visa and your spouse or children are living in Japan together on a "Dpendent", while the you are on leave, your spouse can't earn living expenses on your behalf.
If you have savings just in case, there is no problem, but if you don't, you may want to consider taking out private insurance that will cover part of your living expenses while you are on leave.
Many private insurances allow even foreigners to join if they are not staying in Japan for a short period of time, so why not consider it?