I was using "tbl" as a dummy name for the table because I didn't know what your actual table name was. In your query you would replace the "tbl" with your table name, which is IP_STAYS
--- 1
SELECT a.*,
a.End_Date Current_End_Date,
COALESCE(a.End_Date,b.Start_Date) AS New_End_Date
FROM
IP_STAYS a
LEFT JOIN IP_STAYS b ON
a.Row_ID + 1 = b.Row_ID;
--- 2
UPDATE a SET
a.End_Date = COALESCE(a.End_Date,b.Start_Date)
FROM
IP_STAYS a
LEFT JOIN IP_STAYS b ON
a.Row_ID + 1 = b.Row_ID;