Many people believe that prices skyrocket when artists die, but that's a myth perpetrated primarily by dealers who say anything to make sales. An artist's death significantly impacts his price structure only when he's relatively famous, his work is expensive, he's in demand and collectible, and most importantly, he dies unexpectedly. As evidenced in the months immediately following the deaths of Warhol and Basquiat, for example, their markets went temporarily insane before gradually settling back to normal. Dealers and collectors were caught off guard, everyone scrambled for the art, a sort of buying panic set in, and prices spiked in the upward direction. When an artist dies of old age, however, all market changes have taken place slowly, sensibly, and in an orderly fashion.
Death comes as no surprise to anyone and consequently, prices remain relatively steady.
In some instances, an artist's prices can actually drop on the occasion of his death. For example, an executor or family may mismanage the estate by dumping all the art on the market at once and temporarily depress prices. Another reason for a decline in prices is when collectors patronize an artist more for his personality, media image, flamboyance, social contacts, or sales skills than for the quality of his art. Your main concern should be whether the artist's family or executors are planning on liquidating a large portion of his work within a reasonably short period after his death. Chances of this happening are remote, but if it will make you sleep better at night, check with dealers who represent the artist or if you're feeling exceptionally rude, ask the artist himself.