Executive Orders are only good so long as a successor does not overturn them. Trump, being a racist jerk, made a hobby of undoing anything Obama did. A neat continuance of his "birther" conspiracy hoax. They are warming seats in Hell for that family.
In the U.S., some companies will give "severance" pay to employees whose positions are eliminated due to "downsizing" or other structural reorganizations. That's paid by the employer. There have been scandalous payouts to CEOs that range from stock options to cash payments in the hundreds of millions.
To obtain Unemployment Insurance, you need to go to the relevant State agency with documentation verifying that you weren't outright fired and that the reason you are unemployed is not due to any fault of your own. If eligible, you can receive benefits for a fixed period of time, but normally you have to prove you are actively looking for work during the benefit period to keep receiving the money.