The states that implement vote-by-mail in US (which, coincidentally, uses paper ballots), ensure that the person casting the vote is the person to whom the ballot was mailed by requiring a signature. To implement secret voting, the ballot is enclosed in two envelopes, and only the outer envelope has any personally identifiable information, including said signature. The signature is checked against the one in the voter registration database, and if there's a mismatch, the election department will contact the voter to ensure that the ballot was, in fact, theirs. Once the check is done, the outer envelope is discarded, and the still-sealed ballots are transferred to the people who will actually count them.
This doesn't preclude forcing someone to vote in a certain way, or paying them to vote in a certain way. But that is just as feasible with voting booths with modern tech - you simply demand that the victim records filling the ballot with their smartphone or a similar device. Some countries are banning camera phones from voting booths for this reason, but enforcement is usually impractical.