I am referring to the scenario where militants essentially take over spaces of Pakistan much like they did in Iraq. People from those affected regions may flee wherever they can. Will India cooperate with Pakistan in such a scenario or only ensure that the military propagation continue and let/acquiesce to militants executing innocent civilians fleeing the combat zone if they decide to head east to escape them?
You have left out a whole lot of details on which any GoI will base its decision.
1. For example - have the nuclear weapons been taken out by US/China/International Consortium or secured by the remnant Pakistani Govt.
2. Or are they fair game in their silos with the militants running a race to get to them first.
In case where nuclear weapons have been removed from the situation(point 1), GoI under BJP will be indifferent to Pakistan and seal the borders essentially acquiescing to civilian executions by the terrorists.
GoI under Congress will allow all refugees but not cooperate with Pakistan/minor cooperation in order to prevent complete State collapse.
All the while both making statements supporting Pakistan.
In case where there is a possibility of nuclear weapons falling in the hands of the militants(Scenario 2),
any GoI would support Pakistan as much as possible in whichever way required.
At best if GoI feels opportunistic, BJP may make some demands in return for support, Congress may or may not. But regardless,
both will support the legitimate Govt of Pakistan to prevent a complete State collapse which allows nuclear weapons in the hands of terrorists.
Essentially our best and only aspiration would be to keep Pakistani Punjab and Sindh safer. Because these areas are contiguous to India. Beyond Indus, India wont care much.