Is it possible to heal up a dental fistula without the tooth being pulled?

Sometimes : A fistula forms due to the presence of what is usually an infective or inflammatory reaction of the body. If the tooth has an abscess, then root canal treatment may clear it up.

With root canal: A fistula (or sinus tract) means that there is infection or pus draining from somewhere. You must see the dentist to see where the infection is coming from. If you don't want the tooth extracted, it will need a root canal. It could be a periodontal infection, in which case you still need to see the dentist to find the source of the infection and will likely result in root canal.

Generally, Yes: A dental fistula indicates that an infected tooth has pus coming out through the root, and subsequently through the jaw bone and through the gums into the mouth. If the tooth is not so destroyed that it can be restored, then removing the infection from inside the tooth will allow the fistula to heal. This is commonly known as "root canal treatment." you can remove the infection and keep the tooth.

Fistula: A fistula indicates an active infection. There are several issues that can cause a fistula. Some issues can be addressed using root canal treatment or minor surgical procedures. But, if the reason for the fistula is a vertical root fracture, the chances of saving the tooth are slim to none. Consult your dentist to determine the cause of the fistula and treat immediately.