Only "credit cards" and "debit cards" can be overdrafted; and the cards we usually save money in, called savings cards and "debit cards" cannot be overdrafted.
Rural credit cooperatives also have debit cards and "credit cards". It just depends on which province you are in. For example: Yunnan Rural Credit Cooperatives have credit cards issued and used, and the overdraft limit is relatively large. Personally, I think It's still ok.