Pope John is finished speaking of rights. But rights are a springboard into the principle of a duty. This is a nuance often missed in a narcissistic perspective, when everything seems aligned to feed and nurture the individual.
28. The natural rights of which We have so far been speaking are inextricably bound up with as many duties, all applying to one and the same person. These rights and duties derive their origin, their sustenance, and their indestructibility from the natural law, which in conferring the one imposes the other.
29. Thus, for example, the right to live involves the duty to preserve one’s life; the right to a decent standard of living, the duty to live in a becoming fashion; the right to be free to seek out the truth, the duty to devote oneself to an ever deeper and wider search for it.
I think this can be elaborated a bit more. As a person with a right to live, I have a duty not only to preserve my own life, but to advocate for the defense of the lives of others. My life is not only a personal gift from God, but it is part of a larger gift to all human persons.
Another observation: when Pope John suggests the conferral of one, could he not also mean the conferral of a duty imposes rights on the people of duty? I am given duties as an employee, for example. It might be said that these duties give me certain rights: to exercise my judgment in performing a job, to use resources at hand, to act with other workers to achieve an end, and to receive credit for a completed job well done.