Were there still hunter gatherers in the Neolithic period after farming was invented?
I would most certainly say yes as the hunter gatherer system is deeply ingrained in many societies even today. Some Great Plains Native Americans here in the States are a perfect example of peoples that had a highly developed agricultural society that still participated in hunting buffalo. Even today we see fishing and hunting in many highly industrialized agriculture based nations although more a form of recreation today people still use the food for sustenance. People collecting wild edibles such as mushrooms and wild fruits like blueberries & blackberries are an example of this as well. I think the simplest explanation ultimately is that we as humans have always taken advantage of any available food source to the fullest extent possible throughout history. However, recently in history the impact of industrialized farming has brought the cost of food down so much in highly developed nations that it has become almost more cost effective time wise for individuals to buy all their food
It wouldn`t have ended all at once! There would still have been many remnants of hunter gatherers for many years after farming started. You`ll still find a few even today, in the wilder more remote parts of the world. It is just simply another way to survive, that`s all – if there are still any animals to hunt.