Let $\{a,b\}$ the alphabet $\Sigma$. If $L$ is a language on alphabet $\Sigma$ then i have $$K_L = \{x\,|\,∃y\,|\,(x \sim y \,\land\, y \in L)\}$$ The relation $\sim$ is defined on $\{a,b\}^*$ by $x \sim y$ if $x$ and $y$ have the same number of $a$'s and $b$'s.
So, a word $x \in K_L$ if it can be rearranged to form a word from $L$. I believe that $K_L = A \:\cap\: L^c$ where $A = \{w \::\: |a| = |b| \}$
If i could get a hint as to how to prove that if $L$ is regular, then $K_L$ is always context-free. And maybe some links to help my comprehension. It would be much appreciated !