  The block reversal of a word $w$, denoted by $\mathtt{BR}(w)$, is a
generalization of the concept of the reversal of a word, obtained by
concatenating the blocks of the word in the reverse order. We characterize
non-binary and binary words whose block reversal contains only rich words. We
prove that for a binary word $w$, richness of all elements of $\mathtt{BR}(w)$
depends on $l(w)$, the length of the run sequence of $w$. We show that if all
elements of $\mathtt{BR}(w)$ are rich, then $2\leq l(w)\leq 8$. We also provide
the structure of such words.
