A satisfactory orbital solution for Comet Howard-Koomen-Michels 1979 XI is found on the assumption that the comet's line of apsides coincided with that of the Kreutz sungrazing comet group. The derived perihelion distance then shows that this is the first known case of a comet falling into the sun. A dust tail that survived the comet is studied as a particle flow phenomenon controlled by no force other than solar gravity and solar radiation pressure. The tail's outline is interpreted in terms of an onset of dust production, a peak repulsive force on the particles, and a circumsolar dustfree zone due to particle sublimation. It is shown that the surviving debris consisted mostly of absorbing, submicron size particles in hyperbolic trajectories convex to the sun and curving toward the earth. The tail width may be a product of the interaction of charged dust in the tail with a complicated structure of the coronal magnetic field.