The sail switch is kept closed when the blower is at 75% or higher airflow, so that switch being stuck closed, I don't think would cause the blower to keep running.
After the thermostat set point is reached, the gas valve should close, shutting off the flame/heat, and about 15 seconds later, the control board should cut power to the blower.
So, assuming the gas valve/heat did shut off, you may have a control board problem.