What would you do if you knew a person who had a dog that looks like it has mange - but cannot/will not take her to the vet? It would not be safe to offer ivermectin since she is a x-breed, and likely has collie in her. Is it catching?
Some of our poor coyotes around here look like her
My vet is very approachable but even he would be reluctant to offer something without seeing her...he would help me any way he can.