Employer plans, such as 401ks, require their own EIN. Usually the plan administrator will setup this EIN when the plan itself is developed. Employer retirement plans can vary, from money purchase plans to defined benefit pension plans. Regardless, they are going to be a separate entity from the taxpayer, even if the retirement plan is a solo 401K under a sole proprietorship and they are not under direct control of the taxpayer.
When paying their taxes, taxpayers will get a form that outlines their 401ks benefits and contributions, or the benefits and contributions of their other employer plans. They will file this information under their own taxes, under their own SSN. But they won’t need to track the transactions inside the retirement plan itself, because this is a separate taxpaying entity. They only need to file with the forms they receive. The taxpayer doesn’t need to worry about the management of this EIN, as that is the role of the plan administrator.