Can you lose your driver's license if you owe money because of an accident?

No. Your drivers license may only be temporarily confiscated while the case (related to driving) is under investigation or permanently be revoked or cancelled upon court order. If the court decision involves only penalty or cost of damages, then failure to settle the payment (owe money) may result to the court garnishing (to confiscate) any of your property with value (can be sold or auctioned) to cover the cost of the court-ordered penalty or cost of damages. It will a separate case not related to driving hence does not involved your drivers license card which, by the way, is of no monetary value.