That's not good. Are you doing that? Please stop. If someone in your life is doing that, please tell them to stop. The consequences could be dire.
In most cases, the credit card debt of a deceased American becomes an issue for their estate. If that debtor lives in a community property state (Arizona, California, Idaho, Louisiana, Nevada, New Mexico, Texas, Washington and Wisconsin), then their surviving spouse should seek guidance from an attorney to understand that state's rules. Otherwise, authorized users on credit card accounts aren't liable for leftover balances. Credit card companies write off those debts as a cost of doing business, even though a robust market has opened for third-party collectors who aggressively try to convince loved ones that the debt is theirs to pay. (It's not.)
However, if an authorized user keeps making new purchases on a credit card after the account owner dies, they could wind up on the hook for the remaining debt. Rather than write off the balance, banks often sue authorized users who keep using cards after the primary account holder's death. The lawsuits usually ask for the entire balance, not just the portion charged by an authorized user.
Many state prosecutors also consider this kind of activity a form of fraud, punishable by fines and jail time. A court won't care if you were just trying to be expedient with your short term purchases. If those new purchases also reduce the value of an estate, other beneficiaries could sue you for the value of those transactions, plus penalties and court costs.
Under current banking regulations, most credit card companies will require you to open a new account in your own name instead of just taking over someone else's existing account, even if you intend to pay down the balance. That's true, regardless of the relationship between the primary account holder and the authorized user. Talk to your primary account holder's bank and prepare documentation showing your ability to pay a card's full balance from your own income. Retention agents at many major lenders will want to help you process a balance transfer if you can show that you've been managing the account for some time.