From: https://www.mnsaves.org/documents/mn_disclosure.pdf taken on 2019-09-24
Eligible Beneficiary Any U.S. citizen or resident alien with a valid Social Security
number or taxpayer identification number.
Selecting a Beneficiary You must designate a
Beneficiary on your Application (unless you are a
state or local government or ...
Does your 401k provider stop you when you hit your max?
Here is a bogleheads discussion on the topic. Apparently different employers do different things.
Some employers stop your contributions, some put the money in after-tax 401(k) contributions, and some stop their own matching contributions.