Hospice ordered a Broda Chair for my Husband. He had poor trunk support and the chair was almost like an old fashioned Wing Back chair. the sides supported him a bit more and there were pads or wedges that could be placed in various locations that would prop or support him a bit more. He also had a high back wheelchair at one point that could be reclined a bit so that he did not slump over as much. (when this was no longer as effective that is when they ordered the Broda Chair.)
My MIL is 88 in LTC (on Medicaid) in a facility. She broke her back in 2009, has osteoporosis and immobility. She was having the same problem and the staff got her a different type of wheelchair with a taller back and fitted sides, and seems to have more adjustment options. I apologize I don't know the brand name or what it is called because she's always in it when we visit so I can't ID it by looking at pics online. Just know that there is a solution for this problem.
He also had a high back wheelchair at one point that could be reclined a bit so that he did not slump over as much. (when this was no longer as effective that is when they ordered the Broda Chair.)