SQL Server 2017

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create table jsn (
  Employees nvarchar(max)
);

insert jsn (Employees) 
select 
'{
  "person": "Amy",
  "staff": [
    { "person": "Bill" },
    {
      "person": "Chris",
      "staff": [
        { "person": "Dan" },
        { "person": "Emma" }
      ]
    }
  ]
}';

;WITH hier ([Level], Parent, [Path], Person, staff) AS (
    SELECT 
        1 AS [Level], 
        convert(nvarchar(max),'') AS Parent, 
        convert(nvarchar(max),'/')+l1.person as [Path],
        convert(nvarchar(max),l1.person) as person, 
        l1.staff
    FROM jsn
    cross apply OPENJSON(Employees) WITH (
        person NVARCHAR(max),
        staff NVARCHAR(MAX) AS JSON
    ) l1
UNION ALL 
    select 
        [Level]+1,
        convert(nvarchar(max),h.Person) as Parent,
        h.[Path]+convert(nvarchar(max),'/') + convert(nvarchar(max),oj.person),
        oj.person,
        oj.staff
    from hier h 
    outer apply openjson(h.staff) with (
        person NVARCHAR(max),
        staff NVARCHAR(MAX) AS JSON
    ) oj
    where [Level] < 100 -- or relevant maxrecursion level
        and oj.Person is not null
)
SELECT 
    [Level], 
    Parent, 
    [PATH],
    Person 
FROM hier
order by [Level];

Level	Parent	PATH	Person
1		/Amy	Amy
2	Amy	/Amy/Bill	Bill
2	Amy	/Amy/Chris	Chris
3	Chris	/Amy/Chris/Dan	Dan
3	Chris	/Amy/Chris/Emma	Emma