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To be very honest, there is simply no way to know for sure as it is up to the Governor of Wisconsin to decide whether he wants to incur the time and cost of sending a marshal to transport the defendant back to WI from MN.
But generally, for non-violent offenses that aren't seen as extremely serious offenses, the answer is that the Governor won't extradite simply due to the cost and will just let the holding state release them after notifying them they aren't interested in doing so. The warrant will still remain active indefinitely and each time the defendant comes in contact with law enforcement, the situation will repeat until the person gets back to WI to take care of the charge.
With state budgets in such tight conditions, if the Governor doesn't feel that a person is a serious threat to society and they won't get any public backlash, they will just refuse to extradite.
Obviously this is just my opinion based on 15 years of criminal defense practice..