What will happen to the person?
Can I do self employment?

You CAN file self-employment (Schedule C with Schedule SE) if, in fact, you are self-employed and can prove you earned income in that status.

As for what will happen to the other person? Their return will be audited and adjusted without your personal exemption as a dependent. That's probably the extent of any action taken against them unless this represents a pattern of misconduct on their part.