This bamboo stalk got snapped almost completely in half during a storm two years ago, and yet it still lives.
I can't figure out how it could possibly be drawing enough nutrients to live, and yet there it is. I'd have chopped it up and dragged it away but now I'm impressed and want to see how long it goes on.
If bamboo worked in Animal Crossing the way it does IRL, I'd make sure to never plant any because it would replace weeds faster than weeds appear. You walk out of your house the next day and it'd just be a wall of bamboo. Timmy and Tommy would die of starvation as I am unable to make it to the town center and pay off my debts to them or deliver any fruit.
It really depends on the species of bamboo, and where you plant it. Some bamboo species grow with rhizomes, so once it's established, good luck getting rid of it. IIRC it's golden bamboo that is a problem in the south. But it doesn't grow nearly as fast as people think; it's not kudzu. And it really needs full sun, so it doesn't get established unless it's away from large trees.
There are a few spots on my commute that have been taken over by bamboo. They're pretty isolated from each other. If I was going to guess, I'd say that both were planted intentionally to control erosion.