This is something that does need vet care though some cats will heal on their own its not an easy process and the leg may never work right.
I'm surprised the vet did not splint the leg to keep it from dangling.
Some vets will let you pay on a payment plan and you can ask your vet about that.
You might ask if amputating the leg would be less costly or less painful for the cat.
As cash flow is an issue here are some groups that might help you afford the vet bills:American Animal Hospital Associationhttp://www.aahahelpingpets.org/" Through the AAHA Helping Pets Fund, veterinary care is possible for sick or injured pets even if they have been abandoned or if their owner is experiencing financial hardship."Angels 4 Animalshttp://www.angels4animals.org/"Our services range from financial aid to complete treatmentto those pets and pet owners in need."Care Credithttp://www.carecredit.com/A credit card company for health care, including veterinary care."With a comprehensive range of plan options, fortreatment or procedure fees from $1 to over $25,000, we offer a planand a low monthly payment to fit comfortably into almost everybudget." They have a zero interest program if you pay within a certain time frame and they list the vets who work with their product.God's Creatures Ministryhttp://www.all-creatures.org/gcm/help-cf.html"This fund helps pay for veterinarian bills for those who need help."Help-A-Pethttp://www.help-a-pet.org/home.html http://www.help-a-pet.org/"Our efforts focus on serving the elderly, the disabled, and theworking poor."IMOMhttp://www.imom.org/"We are dedicated to insure that nocompanion animal has to be euthanized simply because their caretakeris financially challenged."The Pet Fundhttp://thepetfund.com/"The Pet Fund is a registered 501(c)3 nonprofit association thatprovides financial assistance to owners of domestic animals who needurgent veterinary care."United Animal Nationshttp://www.uan.org/lifeline/index.html"The m ission of LifeLine is to help homeless or recently rescuedanimals suffering from life-threatening conditions that requirespecific and immediate emergency veterinary care. We strive to serveGood Samaritans and rescue groups who take in sick or injuredanimals. In certain cases, LifeLine can also assist senior citizensand low-income families pay for immediate emergency veterinary care." They also keep a list of local and national help resources herehttp://www.uan.org/index.cfm?navid=163
Feline Veterinary Emergency Assistance (FVEAP)http://www.fveap.org/sys-tmpl/door/"Seniors, People with disabilities, People whohave lost their job, Good Samaritans who rescue a cat or kitten - any of these folks may need financial assistance to save a beloved companion."The Feline Veterinary Emergency Assistance Prog ram is a nonprofit 501(c)(3) organization that provides financial assistance to cat andkitten guardians who are unable to afford veterinary services to savetheir companions when life-threatening illness or injury strikes.
I'm more than happy to answer a follow up and thank you for the above accept. We never 'require' payment though its nice when it happens so no concerns there as you already accepted.
Home splinting may not be a good idea as you might shift bones and cause more damage internal to the leg and unless you really know what you are doing you might accidentally cut off circulation or do other harm.
As this is a knee area this may be a torn cruciate ligament. Info on that here
You can read 4 pages of info on rear leg break care here
If your vet confirmed it was a break then your best option if you can only do home care is to keep the cat very quiet and see if it can possibly heal on its own.
Do check into the groups above though and see if you can get some help.
If you can't then check www.petfinder.com for cat rescue groups in your area - such a group might have someone who would take the cat and do the surgery though it would mean you would lose the cat.