I've heard that nails and hair continue to grow even after death. Is this true or just a myth?
No, this is false.
The University of Arkansas Medical Services debunks this myth:
Hair and fingernails may appear longer after death, but not because they are still growing. Instead, a persons fingernails and hair may appear longer because the skin around them has retracted, according to the Dermatology Clinic at UAMS.
After death, dehydration causes the skin and other soft tissues to shrink. This occurs while the hair and nails remain the same length. This change in the body creates the optical illusion of growth people observe.
The BBC also makes a similar debunking:
So why do myths persist about stubble growing on dead men’s chins and fingernails lengthening? While such observations are false, they do have a biological basis. It is not that the fingernails are growing, but that the skin around them retracts as it becomes dehydrated, making them appear longer. When preparing a body, funeral directors will sometimes moisturise the fingertips to counteract this.