Del. Code tit. 10 § 7356
Whoever is imprisoned for the reasons stated in § 7351 of this title may prefer a petition to the Superior Court setting forth that such person is willing and able to give to the creditor good and sufficient security for the payment of the debt, damages or costs within a reasonable time. If, upon the hearing of the petition, and reasonable notice in writing of the time and place thereof to the party at whose suit the petitioner is imprisoned, or the party's attorney or agent, if there be such party, attorney or agent within the county, it appears that the petitioner is able to give such security, the Court shall proceed to order security to be given and taken in such form, and for the payment of such debt, damages and costs, in such time and manner as to the Court seems meet and proper in the case, and on such security being given and approved by the Court, an order shall be made for the immediate discharge of the petitioner from imprisonment.
10 Del. C. § 7356