The stringiness is the mucousy texture of coccidiosis. People often think blood is *the* symptom of coccidiosis. It's not. That's the symptom that the coccidiosis is at the stage where it can kill. Mucus is the sign that I most look for in coccidiosis. The green might be secondary bacterial inbalance, and in fact I'd bet on it.
Your friend needs to get probiotics down these babies and continue the sulmet. Apple cider vinegar doesn't actually worm - but what it does is inject the systems of the babies (or adults) with some beneficial bacteria. However, you can't mix it in their drinking water with the sulmet. The ACV also helps to correct the pH of the gut so that it's good for good bacteria and unfriendly for bad bacteria.
Incidentally, only organic ACV will have the probiotic effect.
Since she's lost birds, I'd definitely recommend a probiotic and in this case if possible I'd go with one from the grocer or feedstore. Grocer/healthfood store/pharmacy, she'll want acidophilus or better yet capsules to treat women who have yeast infections (as they also contain B. bifidum). From the feedstore: probios, fastrack. In a pinch, she can use a teaspoon of plain (live culture like yoplait or dannon) yogurt or one of the specialized bacteria advertising yogurts mixed in some wetted chick crumbles. remove all food for 30 minutes then replace with this mixture, see that the all eat it.
At 6 weeks old they shouldn't have worms. If they do, something else is wrong. Also make sure your friend's food is medicated with amprolium, not antibiotics. If it's antibiotics and doesn't say amprolium, have her get the right kind. I'm betting it's the right kind though. I'm also betting that these are probably hatchery or feedstore chicks, yes?
Building up the good bacteria is absolutely necessary in these cases. The good bacteria 'colonize' (spread and take hold) and both crowd out bad bacteria as well as making the environment of the gut a bad place for bad bacteria as well as unfriendly for pathogens like the cocci that cause coccidiosis. They also excrete enzymes that help the birds not only digest food better, but ward off bad bacteria (especially E. coli as is the case with B. bifidum which is why I always recommend trying to get something that has that on the label.)
I hope this helps!