First you need to realize that subduction happens over periods of time that the human mind can scarcely comprehend. Hundreds of millions of years. Over periods of time this large, and under immense pressure and temperature, crustal rock that subducts can be considered to act in a ductile or plastic manner similar to the mantle it descends into. Think of soil and soil creep - if you grabbed a handful of soil you'd call it solid material, but over decades or centuries, soil acts in a fluid manner as it creeps laterally under gravity and large stationary objects sink into it. Less than 0.1% of the mantle is thought to be molten, but this is enough to allow its lithic material to act in a ductile manner.

Then you need to understand that as a plate subducts, it is not at all rapidly dissolved or rendered into magma. Some of it does convert to magma and collect in magma chambers that slowly rise due to their buoyancy, which is how you get subduction-related volcanism. Think the suite of volcanoes at the perimeter of the Pacific "Ring of Fire". The immense pressure and heat generated by the spreading and subducting Pacific plate grinding beneath more buoyant crustal plates - with the addition of water and other volatile substances from the ocean - is what generates the magma which eventually rises and produces those volcanoes. Eventually, and over the course of hundreds more millions of years, the subducting plate sinks into the asthenosphere - the uppermost region of the mantle - where it may homogenize with the surrounding lithic material. The ancient Farallon plate, which subducted under the west edge of the North American plate ~50-100 million years ago, is believed to be currently undergoing this process. The plate itself can still be detected with seismological technology.