The last part of Chapter Two is as follows
Therefore, the sage,
makes not acting his thing
and not speaking his religion,
makes myriad things, but without initiating,
gives birth without taking possession,
acts without imposing
gets results without laying claim.
Precisely because he lays no claim, he is not deserted.
The sage is effective yet unobtrusive, gets things done, but with a minimum of fuss. This is the Taoist ideal, to do things but claim no credit.
When it says, "not acting" and "not speaking", what is meant is not endless silence and inactivity, but rather not posing, bragging or doing anything artificial, especially not drawing attention to oneself.The sage has no wish to be the centre of all that happens. He is interested in being of service in ways that facilitate wholesome change and growth, but he has no blue print for others or for how the world should be. He trusts the natural unfolding of things.
無 為 wu wei is a key term in Taoism. It is often translated as "non-action" but a better rendering is probably "not acting", as in acting on the stage. Taoism is about being natural and free from affectation. It sees this not just as a virtue, but more especially as the best way of getting things done, and done in a manner that does not carry within it the seeds of the undoing of what has been done.
In this way, the sage is somewhat like a force of nature that has its effect and then flows on without looking back. This is also the spirit of classicism. Works of skill and beauty are generated, but the author disappears. Lao Tzu would consider we modern people to be obsessed with personality, both our own and that of others. He would have found the creation of celebrities immature and foolish.
The sage does not lay claim to anything, but for this very reason things are drawn to him. People feel safe with him. Therefore, he is not deserted. What he needs comes naturally. Here there is an aspect of trusting in providence. So this is a path that involves little or no calculating, and especially not the calculating of personal advantage. The sage does not ask what is his own personal profit. What comes, comes. Yet because he makes no demands on others, much come naturally.