In a study on what children do at drop off, it was found that there is an emotional crisis about being separated from the caregiver. Typically more of a "mental terror" than a vocalized scream where they believe they will never see their mother or father again. Not surprisingly, this results in one of the most stressful parent-child separations of any activity in a child's day.
As far as how preschools handle these moments with anxious children. Some schools have someone stationed permanently outside who will administer first aid. If needed before calling emergency services and escort them out to their school nurse or other care provider. This strategy has been shown to decrease the need for emergency service transports for injuries related to separation anxiety.