Here is my code, reformatted the way I like to it.

with rCTE as (

select

t1.retained,

t1.dropped,

t1.retained as TopLevel

from

dbo.testing t1

left outer join dbo.testing t2

on t1.retained = t2.dropped

where

t2.dropped is null

union all

select

t1.retained,

t1.dropped,

r.TopLevel

from

dbo.testing t1

inner join rCTE r

on t1.retained = r.dropped)

update tu set

retained = r.TopLevel

from

dbo.testing tu

inner join rCTE r

on tu.retained = r.retained and

tu.dropped = r.dropped;