Del. Code tit. 10 § 5722
Where a party dies after making a written agreement to submit a controversy to arbitration, the proceedings may be begun or continued upon the application of, or upon notice to, the party's executor or administrator, or, where it relates to real property, the party's distributee or devisee who has succeeded to the party's interest in the real property. Where a committee of the property or of the person of a party to such an agreement is appointed, the proceedings may be continued upon the application of, or notice to, the committee. Upon the death or incompetency of a party, the Court may extend the time within which an application to confirm, vacate or modify the award or to stay arbitration must be made. Where a party has died since an award was delivered, the proceedings thereupon are the same as where a party dies after a judgment or decree has been rendered.
10 Del. C. § 5722