Rats can and do kill chickens, and anywhere a rat can go so can any member of the weasel family.
If that photo is the type of setup you have it really isn't up to keeping much of anything away from your birds.
The wood in those pre-fab coops tends to be pretty flimsy or inadequately fastened. Raccoons are freakisly strong and can pretty easily pry thin doors or panels open, especially if there's more than one.
If that's what your run is like a variety of preadators can pretty easily grab a bird through the wire and kill it: hawks, raccoons, foxes. It wouldn't take much for anything to be able to dig under that type of run either.
Your killer could be virtually anything smaller than an adult coyote, and your flock may have fallen victim to multiple predators.
I'm not sure from OP how your ducks managed to survive, but they're probably next on the menu.
When or if you re-stock your flock, invest in one or more trail cameras so you can see what's actually around your property and either make your steup more secure or build something better from scratch.
You shoudln't have any gaps to the outside bigger than 1/2", and the run needs digging prevention either in the form of buried hardware cloth as shown above, or by resting the run on 12 or 14" concrete "pavers".  If you can get your fingertips inside a door and pry it even 1" open it isn't rigid enough to keep preadators out.
Look at the threads on coop and run ideas to find a solution that works for you and fits your budget.