There are several charities that offer assistance with emergency Vet bills. Not wellness vet bills but EMERGENCIES. For instance, the pet was hit by a car or needs emergency bowel obstruction surgery to survive, that sort of thing. I have never used any of these funds personally, but I do know several people that were given help.
I am unsure how comprehensive or current this list is, but it is a great place to start if you need help right now.
Starting a “GoFundMe” page is also a wonderful tool. I know many people that have raised thousands of dollars to assist with Vet bills for emergency cases. You can find out more about that here.