If you're in the US, there is something called CareCredit which you can use for veterinary expenses as well as healthcare needs for yourself and family.
www.carecredit.com
From what I understand, it's basically like a credit card. I have never used it but when I was on a cat forum, many people did use it for expensive unexpected vet bills and it works for them. The CareCredit web site has more info about how the card works and how to qualify if you're over the age of 18.

What is CareCredit? | CareCredit
With CareCredit healthcare financing is made easy. Whether you use your healthcare credit card for your deductible, or to pay for treatments and procedures not covered by insurance, CareCredit helps make the health, wellness and beauty treatments and procedures you want possible today.
From what I understand, it's basically like a credit card. I have never used it but when I was on a cat forum, many people did use it for expensive unexpected vet bills and it works for them. The CareCredit web site has more info about how the card works and how to qualify if you're over the age of 18.