The concept of life-long and life-wide learning is paramount to ubiquitous learning. 

The idea of them is not quite new, as one might think. The notion of life-long and life-wide learning can be traced back to John Dewey. In 1920s, Dewey grew troubled with the current state of affairs in education: where educators were more considered with delivering material more than with the actual student experience with education. In 1938, he suggested that education should be viewed as a life-long entity, not just simply preparing students for life. He based it on two principles: continuity and interaction. Continuity identifies that each experience of a student will echo throughout their life, and interaction acknowledges that influence on students' experience is "situational". (Norman J Jackson, "Lifewide Learning and Education in Universities and Colleges"). 

It very much corresponds with Rousseau's words about didactic education, where he states that experience is paramount to teaching: "Teach your scholar to observe the phenomena of nature; you will soon rouse his curiosity, but if you would have it grow, do not be in too great a hurry to satisfy this curiosity. Put the problems before him and let him solve them himself. Let him know nothing because you have told him, but because he has learnt it for himself. If ever you substitute authority for reason he will cease to reason, he will be a mere plaything of other people’s thoughts". (abstract taken from Bill Cope and Mary Kalantsiz, "Conceptualizing E-learning"). 

In short, education should not be narrowly viewed as something available for students for only a specific timeframe and limited themes; it should deal with the human life as life-long learning process concerning many a subject matters, as education if life. 

As for an example, I would like to give two. First one is my mother studying art and happiness as subjects through Coursera at the age of 55, acing tests and applying the knowledge to her life. Second one is an extremely interesting story as told on TED.