If you find it necessary to help your kitty find a new home, say, for instance, when you have to move and cannot take the cat, there are precautions to take to ensure a best outcome for Miss Kitty or Mr. Cat.
Avoid placing "Free to Good Home" ads anywhere, as this can attract unsavory types to come get the cat and subject the poor thing to a life of horrors, or death. There ARE people who pretend to be nice in order to gather as many unwanted pets as possible in order to sell them to research companies, or their agents. These people are called "bunchers," and usually earn about 20 bucks per pet. The agents get much more from the labs, but the unhappy outcome is that Miss Kitty ends up in a lab being tortured in the name of "science."
You really need to screen people who ask about your pet. And you need to get references, and then CHECK them! Of course, those can be faked, too.
If you can, visit the home and see for yourself if you want your cat to go there.
Ask them questions like, how many cats have they had? How do they feel about declawing, and will they be doing that to your cat? If your cat is an indoor cat, will they be letting her run loose? Do they have dogs? Do they live on a busy street?
It can be helpful to visit with their veterinarian as well to get some outside opinions as to whether they are responsible pet owners.
If you get a "funny feeling" about anything, just back off and tell them you need time to think about it and may not actually give up your cat as you are too attached, etc. Then keep looking.