QuinnyLi my understanding is that if you have segments using folder traits in their rules, then you should not be able to delete the folders. See below:
Delete a Folder Trait
I tried to test with one folder trait containing 1 trait (trait A):
- Created a segment that includes the folder trait
- Then moved the Trait A to another folder
- Then tried deleting the folder trait
- I get blocked with the following message

So at this point despite the folder trait no longer having Trait A in its ranks, you are not able to delete it because it is still linked to the segment rule. To get proper result after you have moved your traits to other folders, you would need to either add the specific traits to the segment rule or change the folder trait to the one they have been moved to.
Apologies if this sounds confusing but hopefully it sheds a bit more light on what is or is not possible in this configuration.