Let's keep it simple.

Instead of paying unemployment to someone immediately after losing their job or their factory closes for two weeks, let's pay unemployment compensation as a match on compensation earned up to a specified amount. For example, if you lose your job, you must find another job (any job, minimum wage or otherwise) before unemployment will start. And it matches your compensation up to a specified amount and for a specified time. This would require those unemployed to seek jobs right away instead of wasting a year pretending to look for a job because they can't seem to find a job that pays what they used to make. It's amazing that people always seem to find jobs when unemployment runs out.

Other ideas?
How about having the option of setting up emergency funds tax free where employees can contribute through payroll deductions? Let the people provide their own unemployment insurance when they lose their jobs. Bypass government all together.

Those who receive unemployment should be required to do at least 25 hours of community service each week so that society receives some benefit.