SQL - Date Range Broken Down by Individual Month and Year while maintaining the ID
You can join against a date dimension table.  I've included a sample Common Table Expression date dimension table - (my sample is for months instead of days).
To create a permanent Date Dimension table (also known as a calendar table), check out this post - Creating a date dimension or calendar table in SQL Server
--demo setup
CREATE TABLE #TEMP
(GRP_ID CHAR(8),
BILL_YR INT,
BEGIN_DT DATETIME,
END_DT DATETIME
)

INSERT INTO #TEMP
(GRP_ID, BILL_YR, BEGIN_DT, END_DT)
VALUES
('12345678','1','2019-01-01','2019-12-31'),
('12345678','2','2020-01-01','2020-12-31')

--common table expression date dimension
;with dates ([Date]) as (
    Select convert(date,'2019-01-01') as [Date] -- Put the start date here

    union all 

    Select dateadd(month, 1, [Date])
    from dates
    where [Date] &lt;= '2020-12-31' -- Put the end date here 
)

select GRP_ID
    ,  BILL_YR
    ,  DATEPART(MONTH,[DATE]) as BEGIN_DT
    ,  DATEPART(YEAR,[DATE]) as END_DT
    from dates d
    join #temp t on d.Date &gt;= t.BEGIN_DT
        and d.Date &lt;= t.END_DT
option (maxrecursion 32767) -- Don't forget to use the maxrecursion option!


| GRP_ID   | BILL_YR | BEGIN_DT | END_DT |
|----------|---------|----------|--------|
| 12345678 | 1       | 1        | 2019   |
| 12345678 | 1       | 2        | 2019   |
| 12345678 | 1       | 3        | 2019   |
| 12345678 | 1       | 4        | 2019   |
| 12345678 | 1       | 5        | 2019   |
| 12345678 | 1       | 6        | 2019   |
| 12345678 | 1       | 7        | 2019   |
| 12345678 | 1       | 8        | 2019   |
| 12345678 | 1       | 9        | 2019   |
| 12345678 | 1       | 10       | 2019   |
| 12345678 | 1       | 11       | 2019   |
| 12345678 | 1       | 12       | 2019   |
| 12345678 | 2       | 1        | 2020   |
| 12345678 | 2       | 2        | 2020   |
| 12345678 | 2       | 3        | 2020   |
| 12345678 | 2       | 4        | 2020   |
| 12345678 | 2       | 5        | 2020   |
| 12345678 | 2       | 6        | 2020   |
| 12345678 | 2       | 7        | 2020   |
| 12345678 | 2       | 8        | 2020   |
| 12345678 | 2       | 9        | 2020   |
| 12345678 | 2       | 10       | 2020   |
| 12345678 | 2       | 11       | 2020   |
| 12345678 | 2       | 12       | 2020   |