Yes, it is legal unless your termination violates an employment agreement, union contract, existing company policy or is in some way discriminatory. Giving notice is a courtesy, not an obligation. And an employer can fire for any reason or no reason at all.Additionally, your employer is not obligted to pay you for the 2 weeks that you are off; it only has to pay for time actually worked. As for unemployment, if you were terminated most states would allow you to collect, however it varies by state. The best thing for you to do now is to apply for unemployment benefits and see if your claim is approved.