Yes, you definitely can because those payment relate to your valid employment. You cannot stay in the USA though.
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Yes, that is a contractual issue, not an immigration one.
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I agree with the previous attorneys, except that currently under the H4 you cannot work. My question would be however is the payment for the non-compete be in the form of a payroll check, is it going to be a lump sum based on the contract. I recommend setting up an appointment with an employment law immigration attorney to discuss further