Del. Code tit. 10 § 365
If, after summons or other process issued out of the Court of Chancery, any defendant therein named does not appear in obedience to the process and according to the rules of such Court, the Court may, on affidavit that such defendant is out of the State, or cannot be found to be served with process and that there is just ground to believe that the defendant intentionally avoids such service, make an order for his or her appearance on a certain day and publish such order as the Court directs not less than once a week for 3 consecutive weeks. If the defendant does not appear, after such publication, according to the order, the Court may enter judgment by default against the nonappearing defendant, and may thereupon issue process to compel the performance either by seizure of the real and personal property of such defendant or part thereof, sufficient to satisfy the plaintiff's demand, or by causing possession of the estate, or effects, demanded by the complaint, to be delivered to the plaintiff, or otherwise, as the case requires. The Court may also order the plaintiff to be paid the demand out of any property so seized, upon plaintiff's giving approved security, in a sufficient sum, to abide any order of the Court for the restitution thereof upon the defendant's appearing to defend the action, and paying such costs as the Court shall order. If such security is not given, the property seized, or whereof possession is ordered to be delivered, shall remain under the direction of the Court in the hands of a receiver or otherwise, until the defendant's appearance, or until such order is made therein as the Court deems is just.
10 Del. C. § 365