I just looked this up because I was curious - I thought total thyroidectomy usually removed any substernal goiter. Apparently it is very rare, but people may have ectopic thyroid tissue in their chest (I'm seeing this referred to as mediastinal goiter), meaning when the thyroid was developing in the fetus, some thyroid tissue developed in a location away from (and unattached to) the thyroid gland. Substernal thyroid after total thyroidectomy can also occur following an "incomplete removal of a plunging goiter".
Here's a case study article about two patients who had this:
Int J Surg Case Rep. 2013; 4(3): 269–271.
Published online 2012 Dec 7. doi: 10.1016/j.ijscr.2012.11.014
The “forgotten” goiter after total thyroidectomy
Alper Sahbaz, Nihat Aksakal, Beyza Ozcinar, Feyyaz Onuray, Kasim Caglayan, and Yesim Erbil⁎
"We report two cases with forgotten goiter. One underwent total thyroidectomy due to thyroid papillary cancer and TSH level was in normal range one month after surgery. The thyroid scintigraphy scan revealed mediastinal thyroid mass. The second case underwent total thyroidectomy due to Graves’ disease and TSH level was low after surgery. At postoperative seventh year, patients were admitted to our Endocrinology Division due to persistent hyperthyroidism and CT scan revealed forgotten thyroid at mediastinum. "