You might have been thinking about Social Security Disability, but once a person turns 62 it's simply Social Security. Yes, her payout will be less than if she could have postponed it for several years, but she'll get what she's earned.
I used to work for an attorney who handled SSDI appeals. What I learned was that the amount of documentation needed is mind-boggling, and the reason most people were turned down at first was that they didn't understand how much documentation they needed. It is absolutely NOT true that Disability claims are always turned down the first time. Things like your age, and exactly what went wrong do factor in. When my brother went blind at age 50 he was immediately accepted for SSDI.
Another thing that people don't understand is that the government tries to figure out if there is any other work that person can possibly do, and if there are jobs of that kind where they live. It's all very complicated.
But to repeat myself, your cousin can simply apply for Social Security and should be getting her first check very quickly.