Recently, I had a very sick hen. She wasn't eating, losing weight, lethargic, weak. I had her on Doxycycline for a week. I suspect she has tumors. But it's a suspicion. I can't know what's going on inside where my eyes can't see. Nor can any of us know what going on inside your hen. So this is what I do when I am considering euthanizing a chicken since I want to be sure I've done everything I can before doing something irreversible.
I tube fed her with raw egg and baby cereal, water, and Nutri-drench and a spoonful of sugar. If she was weak from merely not eating, this should improve a chicken. Next, I gave her a double dose of the strongest antibiotic I had on hand, Cephalexin. I figured if there was no improvement with these strong measures, I would feel confident she wasn't going to respond to anything, and that I could euthanize without second guessing myself that I was doing the right thing.
Well, she made dramatic improvement in 24 hours, and while not cured, she's a lot better. So, I didn't have to euthanize her at this time.
If you do something similar with your hen, you can be confident you've tried everything. Euthanizing your hen may be rough on you, but it's no where near the suffering a terminally sick chicken goes through.