Yes, the autonomic system, keeping heart and lungs working can still keep running, even if the cerebral cortex is completely gone.

The autonomic system is deep in the brain, and is the ladt to go, normally.

ETA: at the point there is no higher brain function (stimulus to light, sound, pain) "You" are essentially dead, but the body can continue to function, since a basic thing is to keep going.

The autonomic systems really will keep going, provided oxygen and food.

Sometimes for years.