Yes a tumor can burst in a dog and kill the dog.
A common tumor that dogs get is Hemangiosarcomas which is a terrible cancer tumor that can easily burst in a dog and kill the dog in a short amount of time.
The Hemangiosarcomas dog tumor can burst and cause massive blood loss which if not treated within minutes can kill the dog.
Some tumors may burst when you don't even know about it.
If a dog has a tumor that is cancerous the dog needs medical attention and surgery if possible to remove the tumor before it spreads, grows larger and kills the dog.
Some tumors may not burst but still kill the dog if the dogs tumor is cancerous.