What is statute of limitations if you live in Arkansas and bill is from Tennessee?

The same. Say for instance you live in Arkansas, and you travel to every other state of the US leaving unpaid bills behind you in every state. The statute of limitations (SoL) is identical in every case. Not because you live in Arkansas, but because the SoL is determined by the Federal Fair Debt Collections Practices Act. Individual states may have shorter or longer SoL's, but the only one that matters is the FFDCPA. How that debt is collected is another matter determined by the collection laws of the individual states.

For instance, it is not possible to garnish the wages of a person who lives in Louisiana, but it is in Michigan. If the debt is in Michigan but the debtor is in Louisiana, too bad; the creditor will not get paid until the debtor pays the debt. If however the debt is in Louisiana, and the debtor is in Michigan, the creditor can attach wages, bank accounts (checking, savings, CDs, IRAs, Mutual Funds, etc), dividends paid by stocks and bonds, Michigan state income taxes, and various other assets that exist in Michigan (or other states that permit such).