If the employee has found something else then he has to notify unemployment himself.
And the employee doesn't have to sign a letter of resignation. The employer can notify unemployment that the employee refused to return to his job, then unemployment will take action.
Even if you don't notify the unemployment office they will know right when you fill out your W-2 and if you continued to collect they will come after you. In this case, he is still unemployed and intends to remain so until it runs out. Every week you have to fill out your claim form where you claim that you didn't refuse any work and looked for work and keep records to prove it (three inquiries per week. This is not enforced. Unless they have some compelling reason to come after you they are not going to check the thousands of claims and verify with every employer you supposedly contacted to check if they got a job application from you. They simply don't have the time or man power.
And in real life this is how it happened, store manager at Ross calls Bill and says, "Hey bud, if you want we're hiring again." Bill says, "Thanks, but I got another gig. Miss you guys. I'll stop by some weekend to say 'Hi'." Bill says, "Good luck, brah. Don't be a stranger."
Nothing comes out of the store manager's pocket. He hires the next kid that walks into the store looking for a job that will pay for his phone, weed, car, and girlfriend while he lives at home. Bill continues to coast for the several more months making over twice the amount before doing nothing before he has to find another entry-level position which he'll get hired for the day he applies because he's clean-cut looking and speaks well. In Hawaii, just being even semi-articulate and being able to string together a coherent sentence in real English is a huge plus.
Life goes on. Hawaii, a socialist State, continues to fall further in debt.
