Yes a colostomy can be taken down but it depends highly on the circumstances of why it was needed in the first place. Sometimes a colostomy is placed as a permanent feature with no possibility of it ever being taken down. Other times it can be temporary. I would need to know the details of the specific case to comment further.
The answer depends on the reason for the bag.
If the anus and rectum have been removed, then it is extremely difficult.
People have done reconstructions in the past but the results were often terrible because nothing can really replace an anal sphincter.
It is such a complex structure that can selectively allow passage of gas without soiling when working perfectly. The reconstructions in the past have often resulted either in difficulty with evacuation or incontinence or under both.
For example, if your colostomy was created because of a low rectal tumor and the resection removed the rectum and the anus, your colostomy is permanent. On the other hand, most colostomies for perforated diverticular disease are reversible. There are circumstances when colostomy reversals are just technically difficult and reversal is aborted. Or if the risk of the surgery outweighs the benefit of reversing it then it is permanent like an elderly person with a bad heart.