Does mind ever stop?
The mind occurs in both passive and active modes. The passive gives
  way to the active when a stimulus is received through one of the sense
  doors. The passive state of mind is called bhava"nga, cuti, or
  paa.tisandhi, according to the occasion.
  
  Bhava"nga. The bhava"nga citta, mentioned earlier, is the primary form
  of mind. It flows from conception to death except when interrupted by
  a stimulus through one of the sense doors. Read more...


The stream of Bhavanga citta is what you have in deep(dreamless) sleep. It is a result of your past birth Karma. The process doesn't stop until the being attains Parinibbana, except in the case of being born in the Asaññasatta realm.