Unemployment insurance helps people who have been laid off from jobs through no fault of their own (if they've worked at them for a while) by providing them with income while they look for new employment. It aids other unemployed people by reducing the competition for jobs because people receiving unemployment payments tend not to look for work as vigorously as people with no income (studies have repeatedly shown this).
Unemployment insurance serves as a stopgap measure for those who lose their jobs due to circumstances beyond their control. The benefits include partial pay, support in obtaining another job, and job re-training if necessary.
It helps them during the time they need it the most. When someone is fired unexpectedly then they have no way to feed their families or pay their bills. Even though you should have a six month backup most people don't make enough money and live paycheck to paycheck. I have never claimed