Rastreando dias contínuos de ausência de dias úteis apenas SQL

Como mencionei no comentário, basta usar um WHERE . Isso é, obviamente, um palpite cego devido à falta de dados de amostra (a amostra não tem dados de horas de trabalho):

--I prefer CTEs over subqueries
WITH CTE AS(
    SELECT s.date_sick,
           s.employee_number,
           ROW_NUMBER() OVER (PARTITION BY employee_number ORDER BY date_sick) AS rn
    FROM dbo.sickness s)
SELECT C.date_sick,
       C.employee_number,
       DENSE_RANK() OVER (ORDER BY C.employee_number, DATEADD(DAY, -C.rn, C.date_sick)) AS sickness_id,
       wh.workinghours
FROM CTE C
     JOIN dbo.workinghours wh ON C.employee_number = wh.employee_number
WHERE wh.working_hours > 0
ORDER BY C.employee_number,
         C.date_sick;