For example, imagine the husband has a very demanding and high income career. The wife stays at home to raise their children, and take care of the home. The wife suddenly passes away.
Now the husband has to hire a nanny, a housekeeper, and possibly a personal assistant to replace the work that was being done; such as, running the errands, taking the kids to school and their activities, dental and doctor visits, grocery shopping, etc.
The cost of replacing all of the efforts of the stay at home mom would be as much as hiring a full-time employee to manage the household.
So, yes, a non-working spouse would definitely need life insurance, in addition to the coverage the working spouse owns. Learn about low cost family life insurance plans.