In 1973, a fire at the National Archives National Personnel Center in St. Louis, destroyed many Korean War Veteran records.  However, following is a list of resources where family members may be able to find surviving records:

Archives.gov

Casualties - National Archives data base (NPRC)
Casualties - State by State list

Draft Records - NPRC Selective Service Records

Missing in Action - The American Battle Monuments Commission (ABMC)

Prisoners of War - National Archives

Numerous other Korean War Resources offered by the NARA