According to reports, there is a phenomenon of married couples getting a divorce, a fictitious divorce, so as to get various benefits from the State that divorced people and single parents benefit from.
source: Globes

This really is nothing really new. I have met people in the past that never officially got married, or rather, never registered their marriage with the State. They did so in order to benefit from single parent welfare payments. I never actually heard of fictitious divorces for that purpose, but it is not so different.

I think a Libertarian would say that it is not the State's business whether or not I am married, and if I don't want to tell them that I am, I shouldn't need to. Divorcing fictitiously seems to be more of a problem because by doing so you are actively stealing from the State taking budgets you shouldn't get (not really different than not registering a marriage but seems to be more proactive to me).

The bigger problem, I think, is the chaos it will create. People living as married but registered as divorced. Who is married? Who is not? There might also be halachic issues or future marriage issues with children born after "divorce".

Also, while I hope this wouldn't happen I do wonder what if such a couple does decide to eventually part ways, how would they then go about dividing up assets and dealing with custody issues? Supposedly they had already been divorced and theoretically dealt with it during the divorce. Can they now go to court to fight about such a division of assets that was already agreed upon differently during the initial "divorce"?