I had a couple ducks do that last year, just before winter. They hatched 6 ducklings between them, so we figured they could take care of them. Within a couple days, there where only 4 babies, so we caught them and brought them into the barn to feed and keep warm.
They where messy at a hole new level that we never imagined possible. So bad that we wont do it again. But the four babies lived and they are doing well.
Chickens will sit all year if you let them. At least mine will that are super broody.