Let $W:=\prod_{i\in \omega} F_i$ be the (external) unrestricted direct product and $U:=\prod_{i\in \omega}^w F_i$ be the (external) restricted direct product of finite groups $F_i$ such that $|F_{i}|<|F_{i+1}|$ for every $i\in\omega$. What can be said about $W/U$? Is $W/U$ residually finite (while $W$ is residually finite), for example?