That is what you want the butterfly bush to do.
It will die in 3-4 years if you let new growth form on the old wood.
Cut dat sumbeech to the ground if you can. hahahahaha
Also with that new growth, cut about a four inch stem below a leaf node and trim off all but the top leaves. Put it in the best potting soil you have but don't let the leaves get wet. Let it get dappled light and no more than 2-3 hours of direct sun a day. Keep the soil moist and don't let it dry out.
We had them in containers everywhere last year.
Edit: hydrangeas (require a dark plastic sack on top of them), butterfly bush, and geraniums are the easiest things for me to propagate from cuttings.
I bought 2 dwarf butterfly "Pugster" blue a few weeks ago. I broke off a couple of stems while transplanting from pot to ground. removed most of the lower leaves and stuck in the ground. Surviving.