Beneficiaries are only responsible for the debts of a deceased person when they already shared the debt obligation — for example, as a cosigner on a loan. Otherwise, the person’s estate, rather than any survivors, must pay off the debt.
All assets, together with their associated responsibilities, become part of your estate. If beneficiaries receive an inheritance they don’t want, such as a real estate timeshare, they may be able to avoid that debt by filing a legal disclaimer refusing that specific gift — an option that should be carefully researched and handled in a timely manner.