Yes it is actually possible for hair to break off and get thin and shorter.
My hair does that in the very center and it acts better when I do clip my dead ends.
Some people say you don't have to trim or clip the dead ends for your hair to grow, in my case you do. You either clip your dead ends or it falls,out off,etc.
I have seen it happen way to many times.
When the ends are trimmed and kept in optimal condition,less hair fall/shed.
You should try getting a hot oil treatment. I won't say a deep conditioner because too much conditioner can make your ends very brittle and continue to break.
I recommend getting a hot oil treatment after getting my ends trimmed and apply it very warm from scalp to ends and let it sit for about 5 to 10 minutes covered and then rinse and style.