I occasionally find an egg that has been dropped in the middle of night (or sometime between bed time and morning).
I also have a couple hens that sleep in a nesting box and I occasionally find an egg that has been laid over night. I don't know how you can stop it though. I imagine the hen is just finishing what she started and didn't finish at "normal" times for whatever reason. It's not that big of a deal.

I'm gonna toss out a few ideas...

Can she get to the nest boxes at all times? If not, get out there earlier and make sure she can. Make sure she has enough light to see early in the morning so she'll come down off the roosts and go to the nest boxes. Are the nest boxes open or enclosed? I've always found that chickens prefer the dark, 'hidey-hole' type nests with a nice deep layer of straw or other nesting material--they like to feel like they are hiding their nests from predators. Nesting material needs to be adequate, too--too little may discourage use of the nests. It could be that bullies are keeping her out of the nest boxes and up on a perch. Providing more nests to make it impossible for the bullies to guard them all at once can help.

If she is young and in her first season of laying, it could just be inexperience.

Velvet ~:>

I have two Easter Egger hens that we purchased from a local farm and raised from chicks. They just began laying eggs a couple of weeks ago, and because we had the one nesting box in the hen house closed off (to prevent them from roosting in it before they were ready to lay), I found the first egg laid in a corner of their outdoor run. It was small but had a strong shell, as have all the subsequent ones as well. I then opened the nest box, added straw and a round rock to show them where to lay and they began to use it right away.

We‘ve been getting eggs almost daily, but since we didn’t know if only one hen was laying or both, we added a camera to the henhouse to be able to watch. They were both laying each day, one earlier in the morning and the other usually late morning, for several weeks. Until last night... I just happened to check the camera late at night to see that at about 1 am one hen had jumped off her perch and laid an egg while standing on the floor of the hen house, even though her nest box was just a foot or so away! I know chickens don’t see well in the dark but still. Well,, the landing cracked the egg but she just stood by it in the dark for nearly 1/2 hour, sometimes checking it but never laying on it. I went out there and retrieved the egg and found it had a slightly gritty shell, unlike all the others they’ve laid which were smooth. The other hen never moved from her perch and seem asleep through it all.

As if that wasn’t odd enough, I checked the cameras when I woke the same day and saw that the OTHER hen also laid an egg, but right from her perch! It also cracked but she never got off her perch. They both came down and out of the henhouse at 6:30 am ignoring the egg, but eventually came back in later and proceeded to eat the egg, shell and all. The one hen who jumped from her perch to lay earlier that morning then began sitting in the nest box, on and off, for about an hour as if she was going to lay again. She didn’t. The other hen never went in the nest box that morning like she usually does. it was all just so odd. One hen laying in the middle of the night can be chalked up to inexperience or just an anomaly, but both doing it on the same night hours apart? What are the odds? Any ideas as to what that was all about?