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Yes it would be unethical and it would be a termination offense if found out. Basically you are double billing for the same time period. If the second job was before or after then it generally is not an issue.
As to the future of hireability, it depends on state labor laws.. but in general a former employer can only verify you worked there, the former employer can not say anything about why you were terminated or even if they would rehire you. If they do, and you find out about it, then that would be grounds for legal action.
My 2 cents..
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