At the time of the 2003 blackout, the NY Times noted: "Insurance may cover some losses, though many companies require a theater production to miss at least two performances before a policy takes effect." I had wondered the other day if this was part of the reason they were so quick to cancel both Saturday AND Sunday shows this time, so that shows would miss at least two shows (the fact that public transportation in NYC wasn't running was obviously a huge factor as well!).
I'd imagine that the insurance covers their costs and salaries for the missed performances, but that's just my guess. NY Times Article
Ken Davenport also touched on this issue in his blog today.
Most Broadway contracts have "force majeure" clauses, which release parties from financial and other obligations in the event of an "act of God", which will give Producers some relief from their responsibilities. The Producer's Perspective