Hmm! I'm in two minds about this one. We have had old ewes up to 20 yrs. They do turn into 'old sticks' but still like pottering around and sunbatheing and hanging out with their chums. Occasionally they will cowp (cast) and be unable to get up on their own. We have found that it is immediate energy they need, and I agree with landroverroy that an energy bucket (molasses) will help. We also go with the fleecewife special of digestive biscuits. The first time you give them you have to break them up and push pieces into the sheep's mouth at the side, just in front of the back teeth and on top of the tongue. They eventually learn to crunch them, then they become addicted, so you can feed maybe half a dozen biscuits, broken into quarters, over the day. Digestives contain sugar, carbs and fibre and help the rumen to keep going, plus providing a good crunch. Feed the browse as well (willow is the best and cow parsley).
What puzzles me is that you say she is fullmouthed so I can't see why she would be so thin. Ours have remained in fine condition until they start to lose their teeth, then when all the teeth are gone they can eat again, with support, but of course you would not breed from her in that state. Have you checked her mouth carefully for wobbly teeth, and signs of abscesses in her back teeth (feel along her jawline on the outside)? If she's not able to pluck grass efficiently ie wobbly teeth which hurt, or chew effectively with the molars then she can appear to be grazing but not actually be taking much in. We also feed our old ladies a tasty coarse mix and they can chew that fine while their back teeth are good, and don't need any front teeth at all.
So, the questions you need to ask are whether she is truly content with her life, and free of pain, or is she doing the sheep thing of pretending she's fine to avoid predation? When she cowps is she distressed or it's just a case of 'woops' then she's ok?
Why are you keeping her alive? Is it for your sake in that you are fond of her and you don't want to face the decision, or are you sure you will know when she's had enough and life is too much of a struggle and you will call the vet or the knackerman?
It sounds like the time is close, but only you can decide on the day. Try the high energy feeds, plus a pain killer from the vet, and see if she improves, and if not make the decision.
Crossposted with PHB - yes, an unshorn fleece, especially if it's wet, can be enough to cowp even a healthy, young sheep