welcome to the forum!
There are ways to fix this, but they're not going to always give 100%. I would take it to several professional rug cleaners in your area. Dont go to a dry cleaner or have the in home services. I may be able to make suggestions on contacts.
silk qum rugs are very special rugs, and should be treated as such. No fun to have to fix this problem, sorry to hear about it
Sounds like quite a rug, do you have images you could post?