In general (there are small differences in procedure, but the basic method is the same) American absentee ballots are put in an envelope by the voter. The ballot itself does not have ANY traceable markings on it. It is a true secret ballot, just like the ballots voted in person in precincts that use paper ballots. (Electronic ballots with no paper trail are a different issue but thankfully, for now, don't apply to absentee voting.) The envelope is where the voter's name/address or other identifying information is written. Often that envelope is then put in a second envelope along with other identity documents, etc - this is the part that varies greatly between jurisdictions.

When the absentee ballots are received, the outer envelope is opened if present and then the validity what's written on the inner envelope plus whatever supplemental materials were enclosed is evaluated according to local rules. The ballot remains inside its sealed envelope at this step and is not examined.

The validation is such things as making sure that someone with that name and address is on the voter rolls, no other ballot has been cast for that person, as well as more nitpicky local requirements like that an affidavit form was signed in the correct places and/or that the signature "matches" the voter's signature on file. If the ballot is accepted at this stage, then and only then is the envelope opened and the ballot put in a ballot box to be counted.

All of this is supervised by elections officials representing both major parties, which in practice makes it very difficult for either side to stuff the ballot box or "lose" ballots. There is still room for suppression via those extra rules - if the local rules are biased towards rejecting any challenged ballot, for example, one party can just claim that people with names they think are less likely to have voted for their side "doesn't match" - this is all highly dependent on the exact jurisdiction you're in and many states have rules biased towards accepting ballots, wherein unless the challenger can present a VERY good reason ("The identified person is dead" for example) the ballot is accepted.

Anything rejected should then get kicked, still unopened, into the "provisional ballot" process which technically has a way for voters to appeal the decision and present evidence that their vote should be counted - this is the same process used for people who aren't on the voter rolls but think they should be, or who weren't able to present any ID at the polls to come back and show their ID the next day, etc. In practice almost no one bothers unless the election-night returns were so close that the provisional votes might actually swing things.

There is, once the ballot has been accepted and the envelope opened, absolutely no way to trace an individual ballot back to a specific person. The ballots themselves may be retained in case there's a recount, but nothing can be "unwound" after a vote is cast.

For in person ballots, after the voter shows their eligibility, they are handed a ballot, or the equivalent such as being authorized to cast one ballot on a voting machine. No identifier stays with the ballot itself in any case; once they've passed the first station and been approved to vote that's it, there is no way to "unwind" or revoke that vote.