Does low thyroglobulin (TG) have any significance?

51F intact thyroid, no history of thyroid cancer or nodules, though ultrasound shows slightly enlarged thyroid, been treated with Unithroid for 10+ years. Doctor said at 2.9, my thyroid is nearly dead. After doing some reading, I have seen that contradicted—either that low TG is a sign thyroid is functioning normally—or that TG is not even considered to be an indicator of thyroid function at all. Can anyone explain?