EXISTS returns a boolean value. So if conditions is true it result in ALL or if condition fails it result in NONE. So if you want to udpate selected rows only then dont use EXISTS at all.

I am not 100% sure what you want but you can try this:

UPDATE LiveTable
SET column = 'string value'
where livetable.columname in (select tablename.columname from tablename(S) left outer join where conditions).