People arrive into Stage Four having spent somewhere around half a century investing themselves in what they believed was meaningful and important. They did great things, worked hard, earned everything they have, maybe started a family or a charity or a political or cultural revolution or two, and now they're done. They've reached the age where their energy and circumstances no longer allow them to pursue their purpose any further.
The goal of Stage Four then becomes not to create a legacy as much as simply making sure that legacy lasts beyond one's death.
This could be something as simple as supporting and advising their (now grown) children and living vicariously through them. It could mean passing on their projects and work to a protégé or apprentice. It could also mean becoming more politically active to maintain their values in a society that they no longer recognize.
Stage Four is important psychologically because it makes the ever-growing reality of one's own mortality more bearable. As humans, we have a deep need to feel as though our lives mean something. This meaning we constantly search for is literally our only psychological defense against the incomprehensibility of this life and the inevitability of our own death. To lose that meaning, or to watch it slip away, or to slowly feel as though the world has left you behind, is to stare oblivion in the face and let it consume you willingly.