Your questions are very illogical and naive, but i'll answer them anyway.
Do you have any idea how many times the Egyptian, Euphratic and other civilizations based on Rivers 'collapsed'?
A 'collapse' does not mean that the inhabitants pack up their bags and go somewhere else. IVC never really (in technical terms) collapsed.
IVC cities faced decline as trade dwindled (due to destabilization in Mesopotamia) and possible Monsoon failure.
These factors made it near-impossible to maintain the cities and a breakdown in urban communities commenced. People simply went back to rural/village life. As prosperity returned, cities on the Indus like Gandhara, Taxila, Sialkot, Multan, Patalla and ect... began to form and would then transform into Kingdoms. These Kingdoms remained independant up till the Achaemenid, Greek and Mauryan invasions.
Not to mention, there was no reason to migrate. River valleys attracted people like a magnet, they were abundant in everything and led to prosperous communities. The Indus is located in such a way that it would deter any migration, to the East and West it is surrounded by the desert - to the North, you have the mountains and to the South, you have the ocean.
There is a reason why people living in the Indus Basin still carry the distinct genealogy of their ancestors.
The only confirmed and relevant migration that took place was towards Central Asia and West Europe from Northern Indus, it's the reason why Punjabs, Pashtuns, Kashmiris and Dardic People share common physical traits with Europeans.
Indo-Aryan Migration theory has been and is being rejected by many scholars and is being dropped out of school syllabuses as we speak.
Even if it did occur, a migration simply does not 'displace' people and there is no evidence that the 'natives' were displaced. Human population was small and the land was huge, there was no need for major resource/land competition. They would've most likely formed their own communities and with the passage of time, absorbed each other.
What stupidity is this? Did the Mughal, British, Arab invasions of India 'kill all the native population' and replace them with Turkic, Arab and White People? There is no archaeological, genetic and historically recorded evidence of a large-scale 'genocide' - there were massacres and city sacks in times of war, but these were all common throughout the world.
The Indus Basin covers majority of Balochistan. The earliest agricultural community on the Indus plains was in Mehrgarh in Balochistan.