By hunkering down on the couch and just losing weight you get the winter scenario. By exercising while you lose weight you get the summer scenario.
To your point, we know lifting weights specifically is crucial for maintaining bone mineral density[1]. I wonder if there’s a correlation between loss of lean mass and reduced bone mineral density.
[1] Crucial being a relative term with respect to the applicability of this study’s findings https://pubmed.ncbi.nlm.nih.gov/31797417/
Edit: for sourcing.
On the other hand the evidence on running and bone density is very consistent.
https://www.nm.org/healthbeat/healthy-tips/fitness/is-runnin...