For your parents to claim you on their tax return as a dependent:
1. They would have to provide more than half of your support and you must be under age 24 and a full-time student if they are claiming you as a qualifying child. OR
2. You must live with them all year, make less than $5,200 and they must provide more than half of your support if they are claiming you as a qualifying relative.
If they do not meet either of these tests, they would not be able to claim you as a dependent on their tax return.
Either way, you will file a tax return to claim your income and would indicate that you are claimed as a dependent on another return if that is the case.
Here is a TurboTax article with the requirements for claiming a dependent
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