Can they? Yes.
Should they? No.
Will you throw them a bone for raising you for 18 years? Up to you.
Realistically, if you file before they do, then you get to claim your exemption. If they file before you do, then you will have to fight it out with the IRS to get it. Generally, the person who files first gets the deduction.
Generally it's better to let them claim you and your education credits; they are probably at a higher tax rate.... and they pay your insurances which you wouldn't be able to cover on 20K income annually. Depending on how much those 2 insurances cost, they may still be paying for over 50% of your support, and rightfully claim you by default.
