I've had this happen twice to my brother kitties. Merry didn't make it. Pippin just had an obstruction of thread a couple of weeks ago and is all better now. Sometimes the wadded up ball is also attached at the other end to the back of the cat's tongue. The string will then gradually tighten as the ball gets passed further down the intestines, which can start making them accordianing over the string. The string will lacerate the soft tissue as the pressure increases. It's pretty awful and you probably caught the problem just in time. Merry was too cut up inside and died shortly after coming out of anesthetic. He was already pretty sick by that point though, so I wouldn't worry about that happening to your kitty.
Radiographs can sometimes show where the stool is and isn't, indicating a blockage, but with the soft, non-metal ingestions, you can't actually see the culprit until the vet goes in for a look.
With any of these type of surgeries, there is a risk of infection, so please when she comes home, follow the vet's advice completely and take her back in if she seems to be doing poorly again. I had to assist feed Pippin for a couple of days after the surgery, but by day 4 he was really perking up. If your kitty isn't eating on her own when she comes home, make sure you get a feeding syringe and food from your vet. She probably hasn't had adequate nutrition for several days and needs food and water to start flowing through her asap.
You may also want to get an E-collar for her. It seems cruel, but you don't want her pulling her stitches/staples out. Pippin started messing with the staples just before we went in to get them out which took about 10 days. He got an E-Collar at that point because they gave him some steroid cream for his scar and they didn't want him to lick at it.
Good luck with your kitty! Keep us up to date on her condition.
Dev & Crew