Your parent's creditors don't care whether she left a will. When your parent dies, her estate has to pay as many of her debts as possible. Dying intestate — without a will — doesn't change that. If the estate runs out of money, you aren't usually responsible for paying off any remaining debts. There are exceptions, however.
When your parent dies intestate, the local probate court appoints an administrator to manage his estate. Like an executor, part of the administrator's job is to notify your parent's creditors so they can file claims against the estate. A creditor who misses the filing deadline set by state law loses the chance to get paid. Creditors who file on time can collect unless the money runs out. Any remaining debts go unpaid.
Unpaid parental debts affect you because they eat into your inheritance. The administrator may even have to sell property you would have inherited in order to pay the creditors. In some cases, the effect is more direct: If you inherit a house with a mortgage, for instance, you inherit the mortgage too. To keep the house, you have to keep up the payments. If you made yourself co-signer or co-borrower for a loan your parent took out, you're responsible if the estate can't pay.
Your parent doesn't have to pass on property using a will. You can inherit without a will, and without going through probate, if you're the beneficiary of an IRA or a living trust, or your parent put your name on a pay-on-death bank account. When you inherit from a living trust or a POD account, your parent's unpaid creditors can go after your inheritance, though it's usually not worth the effort. Federal law protects IRA assets from the owner's creditors, so there's no risk.
You don't inherit until after the administrator pays off all the creditors who file their claims. If the estate doesn't have enough money to pay the debts, you inherit nothing. Even so, you're not liable for the remaining debts. If you loaned your parent some money, you're entitled to get it back from the estate, but you may end up unsatisfied. State law decides who gets paid first; typically, estate administration costs, funeral expenses and taxes come ahead of individual creditors.