Of course, anytime you don't abide by terms of a contractual agreement, you can be sued. That doesn't necessarily mean that they will, and "online" cash advance companies are well known for making baseless threats and saying they will do things that they have no intention to follow through. But, again, you can be sued, and if the Terms and Conditions call for it, which they often do, you would also be responsible for the attorney fees and costs.
Advice on this forum is for informational purposes only and should never be mistaken as a substitute for legal advice. If you are in need of legal advice, you should consult local legal counsel.
The earlier answer is correct: you can be sued if you borrowed money and did not fulfill your obligations under that contract.
However, this debt collector may be violating the law in the way it is threatening you. In North Carolina, debt collectors are specifically forbidden from "[r]epresenting that nonpayment of an alleged debt may result in the arrest of any person." N.C. Gen. Stat. §§ 75-51(5); 58‑70‑95. It sounds like that is exactly what you are being threatened with. If so, you should contact an attorney as soon as possible, because you may have claims against the debt collector.
I am not your lawyer unless you hire me, sign an agreement, and pay my fee. This answer is not legal advice--it is just an attempt to point you towards the resources you need.
If you got a payday loan in North Carolina (while you were in North Carolina), then payday loans are illegal here. In such case, you may want to contact the NC Attorney General. Here is the website: http://www.ncdoj.gov/ or call 1-877-5-NO-SCAM. Here is a link to payday loan information at the Attorney General's website: http://www.ncdoj.gov/Consumer/Credit-and-Loans/Unfair-Loans/Payday-Loans.aspx
Many of these payday lenders, especially those on the internet, are overseas. The chances of these people suing are very slim because of the amounts involved and because it would not be worthwhile for them to hire a lawyer and because such loans, if taken out after 2006, are illegal. They are also difficult to stop when they use harassing tactics because they do not have valid US addresses. Be cautious in dealing with them on your own. It would be better to go through the NC attorney general's office.