THE ACFT WAS OWNED & PILOTED BY A NON-CERTIFICATED PLT WITH TERMINAL CANCER, WHO WAS NOT ELIGIBLE FOR AN FAA MED CERT. WORKERS SAW THE ACFT TAKEOFF AT APRX 1030 EST. ABOUT 1 HR LATER, A NEARBY RESIDENT HEARD WHAT SHE BELIEVED WAS AN ENG 'MISSING' & WENT 'OUTSIDE,' BUT DID NOT SEE ANYTHING. SHE WENT BACK 'INSIDE' & HEARD A LOUD NOISE (BELIEVED TO BE THE THE ACFT CRASHING). SHE WENT 'OUTSIDE' AGAIN, BUT STILL DID NOT SEE ANYTHING. SOON THEREAFTER, THE ACFT WAS OBSERVED WHERE IT HAD CRASHED BESIDE THE APCH END OF RWY 36 AT THE PLT'S PVT STRIP. THERE WAS EVIDENCE IT HAD CRASHED IN A STEEP NOSE DOWN, WINGS LEVEL ATTITUDE. THE ACFT WAS EXTENSIVELY DAMAGED DRG IMPACT. NO PREIMPACT PART FAILURE OR MALFUNCTION OF THE ACFT OR ENG WAS FOUND. ABOUT 20 MI SE AT DOVER AFB, THE WX WAS IN PART: 500' SCATTERED, 900' BROKEN, VIS 2 MI WITH FOG & RAIN. FREEZING RAIN & SNW BGN FALLING SHORTLY AFTER THE ACDNT. THE PLT'S BROTHER BELIEVED THE ACFT ICED UP. THE OWNER/PLT WAS SUFFERING FM THE END STAGE OF LARYNX CANCER WITH COMPLICATIONS OF ANEMIA & HEMOPTYSIS.