Oracle handles this nicely. As long as a cursor is open, you can fetch as many times as necessary and your results will always reflect the point in time at which the cursor was opened. It uses data from the undo logs to virtually rollback changes that were committed after the cursor was opened.
It will work as long as the required rollback data is still available. Eventually the logs get recycled and the rollback data is no longer available, so there is some limit, depending on the log space, system activity, etc.
Unfortunately (IMO), I don’t know of any other DB that works like this. The other databases I’ve worked with use locks to ensure read-consistency, which is problematic if you want read consistency over more than very short duration.