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.
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.)
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.)