Functional equation $f(x+y)\leq yf(x)+f(f(x)).$

Question

Let $f\colon \mathbb{R} \rightarrow \mathbb{R}$ be such that

$$f(x+y)\leq yf(x)+f(f(x)).$$

What can be the restriction of $f$ to $\mathbb{R}_{\leq 0}$