What if she doesn't show up to court?

The gavel goes down, judgment for the plaintiff. (Win by default.)

Yes, joy is correct. She has been summoned to appear, that is contempt of court if she doesn't show up, and plus, she loses.

In addition to the answers you've already received, let's take it a step or two further.

The judge will enter a judgment in favor of Citibank and against your wife. That judgment will be docketed and will start appearing in your wife's credit reports and it will also show on a judgment search. So if your wife is listed on the deed for any property then the judgment will show up in a title search and that property cannot be sold or refinanced unless the judgment is paid in full.

Next, the bank will track down your wife's assets. If she is working her paycheck will be garnished. If her name appears on a bank account that account will be frozen and the money will be withdrawn until the judgment is paid in full.

It does not matter if your name also appears on the property or the bank accounts. They can take the money if your wife's name is on there.