Thirteen days is a long time. I personally would have culled at a week.
Are you willing to pay for a surgery attempt? At this point she's going to die if nothing is done.
My 12-year-old Labrador had a pyometra (infection of the uterus) and the vet advised that she'd likely die simply because of how much pus was in her uterus (she was on the verge of a uterine rupture.) We were given the option of euthanasia, or attempting surgery (which she likely wouldn't survive.) Her age, the infection (bordering on septic,) her weakness, and the chance of rupture all gave her a low likelihood of survival.
This dog had been by my side since I was eight years old, and I wasn't ready to let her go yet. Almost 10k later and she's laying beside me as I write this. It was worth every penny.
My dog, however, doesn't show many signs of aging. She's in incredible health for her age -- no hip dysplasia, no hearing loss, no cataracts, no cancer. If she'd been, say, 14-16 and shown advanced aging symptoms, I'd have likely put her down.
If your hen has been in good health up until this point, then maybe a surgery can be attempted. She can be euthanized, or the vet can attempt a surgery to save her, in which case she still may die on the table. Either way will be a peaceful death, and much better than letting nature drag this out further.
It's up to you, and you have our deepest sympathies for being put in this position.