We trap cats in mostly industrial areas where cats have been dropped off or have found their way to the food we leave for the cats that are there.
If they are feral (born on the streets and never touched by humans) they are spayed and neutered, then returned back to their colonies, and we continue to feed them. If they are tame and have found their way to the food, we are sometimes able to scruff them by the neck, drop them into a carrier, and get them spayed and neutered so they can possibly go to adoptions.
They are then assessed for behavior and health issues. If they do not have adoptable behaviors, i.e. spraying, or they do have health issues, i.e., mouth problems, etc, they will live out their lives at the facility, and be treated for their health issues.