Notification of row entries
An option would be to create an after insert/update trigger which would join the base users table with the virtual inserted table and force the PII columns to be null (or other scrubbing logic).  Here is a very simple example:

--create test table
drop table if exists [dbo].[UserTable]
CREATE TABLE [dbo].[UserTable] (
    [id] [int] NULL
    ,[BirthDate] DATE NULL
    ,[Street1] VARCHAR(30) NULL
    ,[Street2] VARCHAR(30) NULL
    ,[SSN] VARCHAR(9) NULL
    ,[OtherColumn1] VARCHAR(100)
    ,[OtherColumn2] VARCHAR(100)
    ,[OtherColumn3] VARCHAR(100)
    ,
    ) ON [PRIMARY]
GO


--create after insert/update trigger to force PII fields to null
CREATE TRIGGER [dbo].[UserTable_InsertedOrUpdated] ON [dbo].[UserTable]
AFTER INSERT
    ,UPDATE
AS
BEGIN
    SET NOCOUNT ON

    UPDATE ut
    SET ut.birthdate = NULL
        ,ut.Street1 = NULL
        ,ut.Street2 = NULL
        ,ut.SSN = null
    FROM UserTable ut
    JOIN inserted i ON i.id = ut.id
END
GO


--test an insert 
INSERT INTO UserTable (id,Birthdate,Street1,street2,SSN,OtherColumn1,OtherColumn2,OtherColumn3)
VALUES (1,'1960-01-01','Street1','Street2','111111111','OtherColumn1','OtherColumn2','OtherColumn3')
INSERT INTO UserTable (id,Birthdate,Street1,street2,SSN,OtherColumn1,OtherColumn2,OtherColumn3)
VALUES (2,'1960-01-01','Street1','Street2','111111111','OtherColumn1','OtherColumn2','OtherColumn3')

--test an update
UPDATE UserTable
SET SSN = '999' where id = 1

--check the contents of the table
SELECT *
FROM UserTable