This is an inherent risk, particularly in patients whose root canals are severely curved and calcified and/or hard to access. The probability of an occurrence is linked directly to the difficulty of each case.
The broken file in itself will not cause any problems. At this point the thought is that it has become a part of the root canal filling inside the tooth. The key is whether enough bacteria were removed throughout the tooth to allow everything to heal. If you had a large chronic abscess with a lot of swelling and pus, then most endodontists would lean towards more heroic measures to remove the broken file or probably recommend extracting this tooth. One downside to removing a broken file is that you may end up compromising the tooth by trying to remove this little broken piece.
In most cases, research has demonstrated that broken instruments do not affect the over long term success rate of root canals.