I’m sure someone has done it before. The closest that I know is Fibonacci by Splean. There is no rhyme, not really. Every new line starts with about the same word as the previous line ends and then 2 last lines of a verse bring back the first 2 lines. Anyway, just take a look.
When the darkness comes
It comes with silence
In silence I can be myself
In myself I see the darkness
The darkness that brings silence
My brain is full of faulty wires
Wires that make me make mistakes
Mistakes bringing me regrets
Regrets that living in my brain
The brain full of faulty wires
I want to open up my head
Go ahead and take out all the mess
In that mess dig up good parts
Take apart my fears and dreams
I just dream to rewire my head
The head that now holds only mess
I want to find the faulty gear
The broken gear that made me bitter
The biterness of broken heart
In that heart to find love
To love again with no fear
Like no gear ever made me bitter