What is the enveloping action in regards to the story's sense of the "times" and characters' interaction with social currents in "A Hunger Artist"?
Your question seems to point towards the importance placed on the passing of the times and how what is in vogue one moment becomes anachronistic the next moment. Note how this is referenced from the very beginning of the story:
During these last decades the interest in professional fasting has markedly diminished. It used to pay very well to stage such great performances under one's own management, but today that is quite impossible. We live in a different world now.
The tragedy that the hunger artist suffers is shown to be completely outside his control. He and his art are subject to forces greater than he can manipulate: the nature of "entertainment" and what is considered a saleable art form. This understandably creates a sense of massive frustration within the hunger artist as he finds himself, almost overnight, deserted for more poplar attractions. In fact, the text explains, audiences now have a "positive revulsion" for fasting.
Reference is thus made to the fickle nature of the masses and their lack of comprehension of what is "art" and their inability to truly appreciate it when they see it. It is the frustration that the hunger artist experiences that drives him to sublime excess in his art, to fast beyond the time that he had been allowed to, and to finally be able, in an act of defiance, to achieve the ecstatic artistic heights that he has desired to achieve for so long. The irony is of course that he only does this as a forgotten individual, a memento from a previous era, and nobody records his achievement.