The words are all correct, but the meaning is a bit confusing.

Humanitarian health insurance is for those less fortunate in life, such as the orphans, street children, lonely elderly, the disabled, poor and helpless that have no (or little, choose one only) ability to participate in the health insurance program.

It's good to be consistent when listing things. Whe you say" the orphans" then it's good the also put "the" infront of street children, lonely, elderly, the disabled, poor and helpless

Or leave all the rest without "the"

The importantthing is the First one gets the infront of the noun and the rest all or none.

Humanitarian health insurance is for those misfortunes in life,

and have no or little ability to participate in the health insurance program.

I would stick with less fortunate rather than unhappy.

Humanitarian health insurance is for people who are less fortunate in life, such as the orphans, street children, lonely elderly, the disabled, poor and helpless and those without the ability to participate in the health insurance program.

Thank you vere much,Josie.It is useful for me.

Thank Dave!

this is  my another way.What do you think about the translation:

   Humanitarian health insurance is for people who are unhappy in life, such as the orphans, street children, lonely elderly, the disabled, poor and helpless and without any ability to participate in the health insurance program.