Do you think our possible scenario is the right one? Have you heard of people dumping hens in the countryside as they do urban foxes, to fend for themselves in an alien environment?
Yes, people definitely dump hens. We've had a single older hen dropped over our gate before, who I assume was the last one surviving in a garden flock or similar.
We also have half a dozen ducks here who were dumped at a freshly-dug pond at our community woodland. I reckon they were somebody's cute and fluffy lockdown project, but then 'set free' once they got big and messy. The poor things were starving, as there's nothing to eat at a freshly-dug wildlife pond!
What is worse, just last week, our friends found their beloved cockerel badly wounded because somebody had dumped another one over the gate, and they'd spent all afternoon fighting.
So that's three instances I can name. It seems reasonable to deduce that your wee hen is a fourth.