It's not clear what you mean by "didn’t pay in." If your 16-year-old has $4,000 of income on a W-2, and that is his only income, he does not have to file a tax return at all. It doesn't matter whether tax was withheld or not. But if income tax was withheld, he will probably want to file to get a refund of the withheld income tax, even if he is not required to file.
If the $4,000 is on a 1099-NEC or 1099-MISC, or was just cash with no tax form, then he must file a tax return and report the income as self-employment income.
