I haven't researcher Missouri specifically, but from the east coast and throughout the south, a normal way to raise hogs from the 1600s through the 1940s was by freeranging them. I sure it continued past the 1940s, but the practice appears to have curtailed greatly. Growing up in east Texas, my father would turn out the pigs to the bottoms in the morning and go out and gather them up in the evening. Sometimes there would be more, sometimes less. Sometimes they would get with the neighbors to get hogs to their proper owners. No doubt lots escaped during that time as they have throughout the east and south which will account for a good portion of your local population of feral hogs.
See post 28 here for specific references
http://www.thehighroad.org/showthrea...free+range+hog