Once a comet enters our inner solar system, the ice melts and forms long tails that are swept behind them by the solar wind. How much material a comet sheds depends on its size. Comet Hale Bopp, for instance, was huge, with a mass around 10 million million tons, so it survived its passage through the "kill zone" just fine.
Smaller comets, which are more common, have masses around 1,000 tons. These are the bodies that vaporize, usually from the combined factors of sunlight and friction from atmospheric gas.
Comets also shed their mass in different ways, according to Brown et al.'s analysis. "Sunplungers" have orbital paths that reach into the lower atmosphere, about 7,000 kilometers beneath the photosphere.
In this case, sunlight is not the culprit; mass is stripped away by the drag of solar gas that surrounds the comet. This usually happens very rapidly, and such comets are usually destroyed as they collide with the denser layers of the lower solar atmosphere. That kind of explosion should be detectable since they would be similar to solar flares.