Can the old unit directly transfer to employee social security for purchase without the consent of the new unit?

It cannot be handled directly between units.

Unless the new company has transferred you out, your account is in the sealed office of the Social Security Bureau, so another company can directly handle the transfer, but if your new social security company has been paying, the old company can't pay.

Why do you have a new job, and the old unit will help you pay social security? I don't quite understand this.

Provident fund is different from social security. In the provident fund system, as long as the payer has the account number and name of another unit, it can be directly transferred out. However, another unit has to unseal it, or it has been sealed in the unit and has not been issued normally.