Currently all solo chars have their own stash and it is not shared at all.
With 0.9 Solo chars will share their crafting mats, gold and stash.
So I would say it is reasonable to assume, that your Solo stash will remain untouched, even if you migrate your only solo char to normal.
So if you create another Solo char in the future, they would still have access to your previous stash, crafting mats and gold.
Mike confirmed that there will be a functionality to manually wipe your entire solo progress if you want though. (Not sure if that will be mmediately ready for 0.9)