Ever so often, my family and I undertake a small project in our home that requires the tearing out of the old lathe and plaster. Lathe and plaster was used before drywall became the norm. It consisted of wooden slats run horizontally across stud walls and plaster puddied between and over the slats. If you've ever dealt with lathe and plaster, you know the perils of old nails and the heaviness of the plaster. To rid yourself of that mess, you cannot just pick some everyday hefty bag to dispose of the refuse. The nails will tear the bag and the weight will stretch it. For these kinds of disposals, you need a strong bag or a box.
Good luck and happy reusing.