Dusk (1993)

Anne is a figure painter who has been in a melancholy slump for a number of years. She is awakened from this dulled state by news that she only has a year to live. Thus, when she sees an interesting man with a lively appearance during a visit to the library, she decides to try and track him down, perhaps to arrange for a sitting. It turns out that the man is a serial killer, but, given her short life-span, this knowledge does not prevent Anne from developing a relationship with him, though she is understandably skittish around him.