It seems to me that it happens with garments that are made up of multiple parts.
That's exactly right. MD does a physical simulation, Daz does not*.
In MD, the clothing items fall away along the "seams" because the mesh vertexes of the different parts do not actually have edges connecting them. The parts then separate from each other as the forces of gravity, edge tension and internal "pushback" from the figure surface are applied in the simulation.
Daz clothing items can "look okay" when placed on a figure even when the parts are not "connected" to each other because the position is maintained based on the relative offset between the underlying figure rigging and the vertexes of the object parts. (* Dforce does do a "physical" simulation, but I would expect the same result as you see in MD. That's actually the main difference between older clothing and the stuff that is named "Dforce <whatever>" - the creator made sure the seams are linked with edges, and also that there is no pre-existing self interpenetration when the item applied in "A-pose".)
If you wanted to make changes and pull them back into Daz, it's difficult to fix simply because you can't modify the mesh interconnections and still successfully reimport to Daz as a morph.
Regardless of the software, you can't change the mesh net without breaking the UV maps, which means existing object material skins will not work (at least until you re-do the uv maps). When I was last noodling around with 3d stuff, I did not find an easy way to "repair" the uv and still retain the original material layout. That might have just been my skill issue, and/or there might be a better way now.
However if you plan to use the clothing item outside of daz i.e. in blender, or are specifically trying to modify the design, then you'll need to redo the uv/materials anyway.
