The State of Delaware does own both lines, and DCL has long term leases to operate them. I don't think the state can file for abandonment without DCL relinquishing their leases. I also get the feeling that DCL has no intention of relinquishing them. They appear to be rail fans, as well as capable and innovative operators. My opinion is DCL's future looks bright. My hope is a future excursion or two. And there is hope.
Delaware Railway Administration (DelDOT) owns both rail lines operated under contract by Delaware Coast Line.
The 1994 contract was for 5 years (1999) with an option for 5 additional years (2004). MDDE did not take the extension and DCLR regained its contract. So, I am guessing the same applies and it is technically a ten year contract period.