Sorry to hear that there is a fragment left behind at the extraction site. I do agree with Dr Gerald that it sometimes happens to even the best of us. While trying to extract a tooth, sometimes it makes more sense to leave a small little fragment behind, than to scour and cause more damage to the surroundings. Generally if the fragment is small and uninfected, problems shouldn’t arise from it.
After a year (since your surgery was at March 2017), we have to weigh the pros and cons of removing the fragment especially if it’s firmly embedded and hard to access. That would likely be another surgical procedure.
Like Dr Gerald, I wish you a speedy recovery!
Cheers!
Kenneth
