The Dutch Roll is basically a sideslip driven oscillation.
But, in order to drive the dynamic mode which is DR, you need static stability in both the lateral (roll) and directional (yaw) axis.
Directional stability is yawing moment due to sideslip, amongst other things this is driven by wing sweep and the vertical stabiliser (fin!).
Lateral stability is rolling moment due to sideslip, amongst other things this is driven by dihedral, CG below the wing, and wing sweep. Many textbooks refer to lateral stability as "dihedral effect".
If you look along the nose during DR it should describe a figure of eight, whilst if you look along the wingtip it describes an oval. This indicates that it's both roll and yaw related; if you see mostly yaw then directional stability (yaw due to sideslip) is predominant, if you see mostly roll then lateral stability (roll due to sideslip) is predominant.
As to whether it converges (dies out), is neutral (remains about the same) or diverges (becomes larger) is down to the degree of damping, or even if the aircraft's characteristics put more energy into the system.
I have to say, a stalling wing sounds rather extreme to me, possibly in a few oddball cases, but I'd not expect it in general.
To help understand this, imagine rolling a marble down the side of a bowl. Height up the side of the bowl is equivalent to sideslip. If you put some liquid in the bottom, it would be equivalent to increasing damping, if you tapped the marble down each time it came back up the side it would become negatively damped. Gravity is the basic force (static stability) that drives the oscillation.
G