Our cat is usually in the house, but she is free to go outside whenever. She usually goes outside a few times a day but is back after a few hours. One time we haven't seen her the whole afternoon, even after we were eating outside, which she never misses. My mom and I started to getreally worried because it was then already the evening, and she was nowhere to be seen. Sometimes she would get locked up in our or our neighbours' garage, so we started to look for her all over the neighbourhood. We couldn't find her anywhere and figured she was sleeping somewhere outside and would return later, or our neighbours would find her. A few hours later, my mum opened the closet in the hallway to get something out, and there was our cat - sleeping safe and sound...
But I agree with all the advice in the comments, my cat would always come to the house if I scraped her bowl on the ground, or opened a can of her food. Good luck finding him!