My answer is based on Illinois law, because that is where I have experience dealing with these kinds of issues. I am not licensed in Tennessee and the laws may differ. In any event, In Illinois and Michigan anyway, a payday loan company cannot just hire a company to get a warrant against you. They can contact the local prosecutor and try to prosecute you under the local bad checks law (which is pretty rare), or they can sue you for a bad check, or just to get a judgment for the loan you borrowed. If they get a judgment against you, the next step is to either garnish your wages (if that is possible) or do a Citation to discover assets. If you do not appear at a Citation to discover assets hearing (in Illinois anyway) a Rule to Show Cause may be issued by the court. The purpose of this Rule, would be to find out why you shouldn't be found in contempt for failing to appear at the Citation to discover assets. If you do not appear at the hearing date for the Rule to Show Cause, then the court may issue a body attachment (this is what it is called in Illinois), with a bond amount. While it has the same effect as a warrant for one's arrest, payment of the bond amount will keep you from being kept in jail for any amount of time. There would then be a bond turnover hearing, and the bond is typically turned over to pay toward the debt (it is rarely sufficient to pay the entire debt).
If you are being told they will put you in jail, keep in mind the only way that can happen is how I described above (and that is assuming that this process occurs in Tennessee, which I do not know if it does). If you always appear in court when told to, and cooperate with the lender, there is no way you will have a warrant issued. Any time a creditor calls and tells you they are going to put you in jail, get their contact info, and contact a local consumer law attorney to see if you have a claim against the company. It is not okay to be threatened to be put in jail when it is not true. Additionally, you need to seek a local attorney to verify what the process is in Tennessee for collections, as it is likely that it is not the same as Illinois.