Here's a proposal. Set up a permanent colony around Centauri A or B.
The rational declining civilization says we can't do this. The distance is too far, requiring several generations of man to get there. If it were a multi-generational colony craft capable of sustained 1G acceleration to minimize travel time without damaging the living occupants, the vessel would be immense and thus far too expensive. Besides, we have no idea about the conditions of planets in and around these stars, if there are any.
Let's do something more convenient and pressing like save Darfur. We the people appreciate quick gratification, we feel more secure with a low probability of failure and we can live with tiny gains that vanish quickly in due time.
The ascending civilization says let's go for it. No, we won't come anywhere close right now, but maybe we can take one step. Let's get a handle on setting up a long term colony closer to home on Earth's moon.
After the first generation, we lost some people and wealth, but finally we have a handle on this long term space colony thing. Tourists who save up $25k for our "Vacation of a Lifetime" have started to show up, taking some of the financial pressure off. People are talking about setting up moisture farms as independent pioneer colonists.
After the second generation, we're getting better at keeping people from dying on the moon, but the profit from space tourism is tapering off because the price tag is less. But, the moisture farms are popping up alongside some unexpected mineral farms and greenhouses. This moon colony thing is looking like a permanent self-sustaining operation. People are talking about having a go at Mars.
After the third generation, a fairly active spaceport appears on the moon shuttling people between the moon surface, the independent but struggling LaGrange Point colonies that have appeared, and the aging but busy International Space Station in close Earth orbit. The first long term Mars outpost looks like a winner after the preceding four went bust. People are talking about mining water ice and metals from the distant asteroid belt.
After the fourth generation, a couple of long term colonies are set up on Mars. Additionally, there is a gritty spacecraft refueling and maintenance station sheltered in a crater on the surface of Phobos. Several premature expeditions to the asteroid belt were disasters. Some of them are unaccounted for. We have no idea where they are. One made it back intact, but empty handed, except for a wealth of data on local conditions in that remote part of the Solar System.
The Alpha Centauri thing is still totally unrealistic, but we're keeping our heading fixed in that direction nonetheless. It's a step-and-a-half backward for every two steps forward, but we're finally conquering places those who came before us could never hope to master.