Suppose that we have a $\lambda$-combinatorial model category $M$ (for some cardinal $\lambda$) such that any $\lambda$-filtered colimit of fibrant-cofibrant objects is always fibrant. My question is the following: It is true that any fibrant object in $M$ is a filtered colimit of fibrant-cofibrant objects ?
Edit: After reading the comments, I have realized that I have to add some reasonable condition. So here is the additional condition. Let $R:M\rightarrow M$ be a functorial fibrant replacement i.e. for any $x\in M$ we have a functorial factorization $x\rightarrow R(x)\rightarrow 1$ there the first map is a trivial cofibration and the second map fibration (1 is terminal object).
So here is my new question: It is true that for any object $x\in M$, $R(x)$ is a $\lambda$-filtered colimit of fibrant-cofibrant objects ?