Depending on the region, it may continue to grow if the weather permits and the plant goes untouched. Id imagine that the plant would die in colder climates. As far as the bud....not sure. It'll probably fall offas the weather gets colder. If in a war climate they may continue to bud until the got too heavy and just fell to the ground.

Now wouldnt that be nice to stumble on a wild plant with buds falling off it!