Work without being paid any money.
"Payed" - NEVER with money or things of value!
"Paid" - ALWAYS with money or thing of value!
"Payed" is a past tense of pay but as Zora states, "to let out a cable or line." and that is it.
The line payed out because it was too short. Use payed with out
All it is missing is a subject in the original sentence. Who works with being paid any money?
We work without being paid any money.
It reminds me of my Spanish-speaking student who always says "No sabo" instead of "No s�"