It is not illegal for an exempt employee to handle non-exempt tasks. If more than 50% of the work the employee does in any given week is non-exempt, then FOR THAT WEEK ONLY the exemption is lost and the employee is due overtime. However, the law does NOT say that exempt employees can never handle any non-exempt duties. It is a rare exempt position that doesn't include SOME non-exempt tasks as a regular thing.
This answer remains the same regardless of industry or state. Turning it around is not going to get you a different answer.
If you quit you don't get unemployment.

