Or will they send a check?
Your unemployment compensation funds go into a bank account, that is tied to the debit card. If you lose the card, the funds still get deposited to that account. You will not receive a check. If you lost the card, you'll need to file for a replacement card (will have the same number and pin as the previous card). Unemployment usually goes to your personal bank, not to a state account. Therefore you'd normally contact your bank for a replacement card.