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If you don't have an employment contract stating that you can only be terminated for cause, then yes they can.
This is called 'at will' employment, which means you can legally be terminated at any time, with or without cause. Now, I will say that resigning is a trap. If you resign, they don't get to decide that you get unemployment. The state makes that determination and if the states knows that you resigned, you'll be disqualified for unemployment.
However, if you are actually terminated, the employer has to prove "cause" to be able to block your unemployment, either through evidence of your breaking company policy or some other clear example of misconduct. The burden would be on them then, so I do not think it is wise to resign.