We cannot comment on New Jersey law in particular, but you can probably simply explain to the state that there’s nothing in your mother’s estate. The state does have the right to recover from your mother’s estate whatever it has paid for her care under the Medicaid program. However, that claim is only for what your mother may have owned. The claim is not against you and your siblings. But to be certain of this answer, you would need to consult with a New Jersey elder law attorney.
For more on Medicaid's power to recoup benefits paid, click here.