No. Such content is vulgar and inappropriate for public sharing. It violates moral and ethical norms and may also be against the rules of many platforms.
We should firmly oppose it. If it's on a platform, report it so that the platform can take appropriate action to remove or restrict such inappropriate content.
I don't have a specific story about a 'big cock neighbor' right now. It could be a story about a neighbor who has a large rooster as a pet. Maybe the rooster crows very loudly every morning and at first it annoys the other neighbors, but over time they get used to it and even start to find it charming in a way.
A woman was always intrigued by her neighbor's big cock. One afternoon, she was sitting on her porch and saw the neighbor bring out the big cock. It was a magnificent specimen. As she watched surreptitiously, she noticed how the big cock was treated with special care. The neighbor fed it some special grains and talked to it gently. The woman realized that the big cock was not just a big bird, but also a beloved pet to the neighbor. She continued to watch from time to time, always finding something new and interesting about the big cock and its relationship with the neighbor.
No, it's not a common phrase at all. In normal English usage, it seems rather strange and not a typical expression you would hear in everyday conversation or see in general writing.
One good neighbor story could be that my neighbor noticed I had left my car lights on one night. He came over and knocked on my door to let me know so that my battery wouldn't die. It was a simple act of kindness but really made my day.
I'm not sure if there is a specific 'big cock harry neighbor she fanfiction' available. Fanfiction is a vast genre and there are many different works out there. You could try searching on major fanfiction websites like Archive of Our Own or FanFiction.net, but it's also possible that the title you mentioned might be very specific or not commonly found.