It depends on state law.
However, in your resident state, you're taxed on all your worldwide income, and generally losses in a different state should be able to offset profits in your resident state.
In the non-resident state, this is probably where you'll see more variation in state law. But I think in the majority of states, you take your federal AGI, which consists of whatever specific items were allowed according to the various limitations such as passive activity loss rules, and you'll take each specific allowed item and say whether it happened in that state or not. Based on that, you'll figure what percentage of the total income happened in the state and go from there, figuring the tax amount accordingly.
So in your situation, assuming that the taxpayer is a non-resident in the "new state," you'll probably be looking at the profit in the new state being a larger percentage of the federal AGI than what you feel like is fair (because of the PAL's in the other state). But in any case, that income happened in that state, and they'll want tax on it. But the good news is that you'll probably also get to claim a larger percentage of itemized deductions, exemptions, etc., since such as high percentage of the income was in that state.