Below is pictured the bottom stub on an Ohio ballot. If you are mailing in a ballot, dropping off at a drop box your instructions are to "do not remove this stub".
EDITED TO ADD: This picture (below) is of the envelope into which the ballot is placed (so-called authentication or security envelope). Notice that printed on this envelope (circled in red) is preprinted the voter's name and the same numbers that appear on the ballot (28969). It gives the appearance that this number is assigned to not only the ballot but the voter.