Extradition for nonpayment of alimony is a rare event, but there's no state in the union where extradition is impossible. All 50 states have signed the Uniform Interstate Family Support Act into law, and UIFSA makes it possible to extradite an ex-spouse for nonpayment of alimony. Even without extradition, states can enforce spousal-support payments against former residents who've fled across their borders.
Faced with a state court decision ordering them to pay spousal or child support, some parents have tried to move to another state outside the court's jurisdiction. In the 20th century, Congress passed a series of laws to make it easier to enforce divorce judgments across state lines. States have different rules on alimony and child support, but under UIFSA, if a judge imposes a spousal-support order, the laws of that state usually trump those of the state in which the debtor resides.
The Constitution states that any person charged with a crime "who shall flee from Justice, and be found in another State" can be returned to the state with jurisdiction over the crime. This doesn't happen automatically; the presiding state must make an official request for extradition along with a copy of the relevant court indictment or affidavit. Under UIFSA, a state can extradite someone if she's facing criminal charges for nonpayment of family support. This is a rare last resort, however.
Under UIFSA, a state can enforce its courts' family support judgments without resorting to extradition. The court handling the case can file certified copies of the judgment in the state where the nonpaying individual resides. The courts there can then take action, such as garnishing the debtor's wages or issuing a contempt citation. While child support actions can be modified outside the state that imposed them, spousal support decrees, in most cases, cannot.
If one spouse is already out of state when the other requests spousal support, the question of which state's courts have authority will have to be decided on a case-by-case basis. The Uniform Interstate Family Support Act gives a list of "long arm" provisions that establish the authority of one state to make support decisions affecting a resident of another state. Once the authority is established, the appropriate state courts can proceed to issue a support judgment, which will be enforced under the UIFSA.