"Arc" by the ubiquitous Hugo and Nebula award winner Ken Liu appeared in the September/October 2012 issue of Fantasy & Science Fiction. "A wayward teenaged girl leaves home, learns tough life lessons, develops a talent for artistically preserving partially dissected cadavers, and eventually faces a unique dilemma when she becomes the first recipient of life prolongation treatments."
The story moves slowly and does not become speculative until the final quarter of it. The language waxes poetic at times, typical of the author, which I enjoy, but some may find off-putting. There is no clear trajectory; the prolongation treatment aspect of the story particularly comes as somewhat of a shock. There appears to be an attempt at a moral lesson or two--"love never lasts," and "living forever may not be all that desirable"--but they do not mesh together and seem a bit tacked on.