Is it possible for an iv needle/catheter to break off in vein and what would be the consequences and intervention if so?

Yes, possible.: It would be unusual for an IV needle to break, but a plastic catheter could. It might(doubtful) migrate into a bigger vein and have to be retrieved by an interventional radiologist or a vascular surgeon. Again this would be a rare event.

Yes: They can break but rare. They will break if they are not in the vein usually and they will get stuck under the skin , even if they break in the vein there is nothing to do surgically . But you have to watch for signs of infection at the site like redness , swelling , pain . That means it is getting infected and need to be removed. Very rarely they will move from the vein toward the heart.