If your cousin supported you and you lived with them ALL YEAR, your cousin may be able to claim you and get the $500 credit for other dependents. If you are claimed as a dependent you will not receive the stimulus check.
IRS interview to help determine who can be claimed:
https://www.irs.gov/help/ita/who-can-i-claim-as-a-dependent
CREDIT FOR OTHER DEPENDENTS
It is best if you file for yourself with ZERO income, and the stimulus package.
WhileI was unemployed all year of 2019, I only lived with him for 8 month of 2019.
He has already filed and claimed me.
What should I do?
Try filing either a "zero" return or go on the IRS non-filer site. The IRS will have to sort it out. Good luck.
IRS PORTAL FOR NON-FILERS
https://www.irs.gov/coronavirus/non-filers-enter-payment-info-here
https://ttlc.intuit.com/community/tax-topics/help/how-will-the-stimulus-package-impact-me/00/1393859
https://turbotax.intuit.com/stimulus-check/