I can't remember the name of this story or where I first read or heard
it.  These are the only details that I remember and they might be
wrong:

A young girl inherits her wealthy father's (or family's) house. 
Although she has all these possessions, she is still unhappy.  Somehow
she learns about this man who reached enlightenment by meditating for
a number of years or was it days???  She decides to give away all her
possessions (except the house) and meditate in silence to try and
reach enlightenment.  After many years, this man learns that a girl
has been meditating in silence for several years and goes to meet her.
 I don't remember the ending very well except that he tells her that
nobody has ever meditated this long before... or something to that
effect and that he only meditated for several days - not years!  Then
he kissed her forehead and her frail body caved in.  It was actually a
really nice story, if only I could find it again to read.