What happens if I fail to anwer to a summon to file with the clerks office?

Depends on what kind of case and the state, but generally, if this is a civil case (suit for money), what happens is a default judgment will be entered for the amount sued for (or for whatever amount the plaintiff can prove if it's not a suit for a fixed sum). The plaintiff can then try to collect by garnishing wages (in most states) or bank accounts, or levying on assets. They may also then be entitled to require a personal appearance to answer questions about assets, and the judgment debtor can be arrested for failing to respond to that, but not to the initial lawsuit. Now, I'm assuming this is a civil case because you state a "summons to file with the clerk's office" rather than a summons to appear - if it's not a civil case, or if your mom was ordered to appear, there may be different/more serious consequences for failing to comply.

You can be arrested and brought into court on the next court day. If you are arrested on a Friday night then you will be held until Monday morning in jail.

Worst case? Yes she will go for FTA. Up to the court that issues it.