Veronika Decides to Die
(2009)

Veronika attempts suicide.  She becomes a media sensation because she writes her suicide note to a magazine over an article about green being the new black after she finds herself unable to write a note to her parents.  

She wakes up in a facility and is told by her doctor that in the attempt she damaged her heart severely and *could* die at any time.  He tells her that they don't expect her to last more than a week or two.  This is a lie: the doctor has show her another patient's heart scan in an effort to get her to want to live because she believes she's dying or could at any moment.

As a result, Veronika falls in love with another patient who is/has been ready to leave for quite awhile.  She starts playing the piano again too.  She, essentially, recovers because of this belief.  The doctor expresses no regrets in lying to her -- figuring she might find out the truth later, but for the time being she will live in the moment.

Thanks Linsey!