At that point they are ready to start assuming some responsibility for asking to use the toilet. Even then they should be asked regularly if they need to go. Some children will start to have an increased frequency of accidents after they are well trained because, in their effort to master control over these bodily functions, they try to hold it as long as possible, and when they finally become overwhelmed by the urge, they can't get to the bathroom in time. They will need to be reminded not to wait too long. It would also be wise to try to get them to use the bathroom before becoming involved in any long activity.
Constipation is the enemy of bowel training.
Children who are constipated have difficulty having bowel movements to begin with, and so, are more resistant to having their bowel movements into the potty. They don't have the patience to sit and strain on the bowl when, in their minds, they already know that pooping in their diapers will work. It is best to have those children on high fiber diets including bran and prunes, and fruit juice, including prune juice. Most children don't have bowel movements during sleep, but many wet themselves while they are asleep. This is called enuresis.