R.I. Gen. Laws § 44-33-4

The right to file a claim under this chapter is personal to the claimant and shall not survive his or her death, but the right may be exercised on behalf of a claimant by his or her legal guardian or attorney-in-fact. If a claimant dies after having filed a timely claim, the amount of the claim is disbursed to another member of the household as determined by the tax administrator. If the claimant was the only member of his or her household, the claim may be paid to his or her executor or administrator, but if neither is appointed and qualified within two (2) years of the filing of the claim, the amount of the claim shall escheat to the state.