The tail end of noun phrase collocation
The word "tail" can be subtituted by "tag" without changing the meaning.
The ending or hindmost part of something.
I didn't realize the speaker was my old friend until the tail end of her speech,
At the tail end of the lesson, everyone seems to be exhausted.
My performance is at the tail end of the list.
The hindmost part of a person or animal
There are strange spots that has appeard at the tail end of my cat.
This phrase usually goes after "at".
I am going to pay a visit to Japan at the tail end of this month.
To encounter bad luck, or being picked doing something undesirable
Mike drew the short straw and had to clean the bathroom