I am not too sure that I fully understand what you mean by "pathetic responsibility." Are you talking about the impact that Azucena has on Rolf Carle's life through their brief but profound friendship? If I am incorrect with this assumption, please write back to me giving a definition of this phrase.
However, if this is the case, it is clear that Azucena, although she is so young, fragile and tender, has an incredible impact on Rolf Carle's life. As Rolf joins Azucena on the journey of her last few hours and tries to struggle to save her from death, her suffering that he witnesses unlocks his own repressed suffering, and lets it loose in one tremendous surge. Consider what the story tells us about this process:
That night, imperceptibly, the unyielding floodgates that had contained Rolf Carle's past for so many years began to open, and the torrent of all that had lain hidden in the deepest and most secret layers of memory poured out, leveling before it the obstacles that had blocked his consciousness for so long.
This, surely is Azucena's "pathetic responsibility." Unknowingly, the way that she bonds so closely with Rolf Carle forces him to acknowledge his own suffering and pain, and through this, to rise above it. As he accepts Azucena's death and says goodbye to her, note what happens to both of them:
I felt how in that instant both were saved from despair, how they were freed from the clay, how they rose above the vultures and helicopters, how togethery they flew above the vast swamp of corruption and laments. How, finally, they were able to accept death.
Rolf Carle emerges from this experience a changed man, but a man who is better for having befriended Azucena and for spending her last hours on this earth with her.