Not sure I understand your question, but without thyroid glands, the only thyroid in her blood will be from meds.
She doesnt have a thyroid at all. It was removed due to cancer. So, would she have biologically produced Throid hormones?
If she is not balance with meds and she still is exhaysted - have someone check the Free T3 lab.
Slow metobolism and fatigue are very common when this lab is low ( for her)
Read more information on the Free T3 and the Free T4 lab and have the doctor stop using TSH as there guide to her being optimal.
It would be wise - if this has been an ongoing issue to have her adrenals checked too.
Trying to treat a hypo patient by adjusting meds based on TSH is just wrong. TSH is a pituitary hormone that does not correlate very well at all with hypo symptoms. Far better would be for the doctor to listen to your friend's remaining symptoms, and test and adjust the actual , biologically active thyroid hormones (FT3 and FT4), with meds, as required to alleviate those symptoms. Frequently this requires that FT3 and FT4 are adjusted into the upper part of their reference ranges.
So, first thing I suggest is to go and get tested for FT3 and FT4 (not to be confused with total T3 and total T4), and find out if her doctor is agreeable to treating her symptoms as described above, rather than relying only on TSH.
Here is a good link for you to read through.
http://www.hormonerestoration.com/Thyroid.html