Can social security re-open an account across cities in the province?

No, you can only renew it. You only have one ID number, which is recorded in the national social security network. You can continue to provide the ID number to pay in the new unit. If you have no job, you can go to the social security center to renew your insurance.

However, some social security agencies need your previous unit to issue a resignation certificate, allowing you to re-pay social security.

They are mainly trying to avoid responsibility, which needs to be implemented in combination with your local laws and regulations. However, I suggest that after you pay a new insurance, you should merge the previous insurance. The original unit will give you a certificate of termination of the labor contract, a bill of payment and related social security cards, and hand them over to the personnel department of the new company, which will help you with the insurance transfer.