I think situation depends on if any sort of business-use assets were involved while self-employed. If any depreciation of a business property (e.g. office space, car, computer, etc.) were claimed on previous tax returns (through IRS form 4562) , you have to dispose of business property by selling it or converting it back to personal-use property in order to exit the business. If no assets were involved - you can probably claim that you are exiting self-employed business any time as long as it stops generating revenue, at least for a given tax year. Then claim your unemployment benefits. I think that you have to be self-employed for at least 6 months and make quarterly estimated tax payments to qualify for unemployment benefits.
You can check with IRS publications on that and can contact Unemployment office for clarification.