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Hello, this is Dr. Jess. I am so sorry to hear about your situation! Can you tell me how long ago your kitty ate the string? How long is the string? And how long ago did she vomit?
It appears that you may not be online to discuss your kitty right now, but I will reply here in case you check back in later. Some cats are able to pass foreign objects like string or ribbon, but we do always worry very much about the possibility of obstruction and plication of the intestines especially with linear objects. Unfortunately, if your kitty has vomited and the string hasn't come up, the recommendation would be to have him seen ASAP by a veterinarian. If he had not yet vomited we may consider giving him an oral laxative such as laxatone http://www.petco.com/shop/en/petcostore/tomlyn-laxatone-tuna-flavored-hairball-lubricant and monitoring closely for the next 48 hours for signs of a problem, which would include decreased appetite, lethargy, abdominal pain, straining to have a bowel movement, and vomiting. Unfortunately, your kitty has already shown a concerning symptom, which is vomiting, and so the safest thing would be to have him examined by your vet or an emergency vet if your vet doesn't have openings or isn't available.
Please let me know if you have additional questions.