If only a few hundred Human colonists make it into self-sufficient space colonies before economical collapse cripples Earth-based space activity, the colonists may, after establishing themselves in space, help the Humans who are stuck on Earth, or those of them who want, to leave Earth. See also manipulated spacetimes and the anti-congestion argument.
The grand rescue concept can also economically be considered a variety of better launches. That is, fueled-and-ready spacecraft are mass-produced in space using the abundance of resources out there. Those spacecraft are then sent down to Earth and used for launches from Earth. That would make space travel inexpensive to anyone, enabling large-scale space colonization. Therefore a main aim of the space colonization movement must be to establish a few bases in space from which the abundance of resources can be used for cheaply mass-producing spacecraft.
The spacecraft could be in the form of space planes that uses the atmosphere as a help in the beginning and also use atmospheric oxygen early in the launch, so the oxygen tank can be made smaller (which saves fuel as well due to reduced weight). The fuel, hydrogen, can be taken from gas giants, most practically Saturn due to lowest gravity of all gas giants, less radiation than Jupiter and less other elements (and closer proximity) than Uranus and Neptune. The oxygen can be taken from farms in space, and the spacecraft can also be delivered in the same way as food from space.