Ballots can certainly be lost or delayed in the mail. Ballots can be delivered successfully but rejected because the signature didn't match what the state had on file. Rarely, ballots can also be misplaced. Ballots can also be rejected because of issues with the postmark but presumably not if you're looking to see whether your ballot was accepted prior to election day. And, again presumably not what was being referenced in the quote, there can be issues with a particular ballot that may cause it not to count-- things like voting for multiple candidates, voting for a candidate but then writing in that same candidate, etc. These are the sorts of issues that were at issue in the 2000 Bush v Gore Florida recount. In the most recent New York primary, more than 20% of the ballots that were delivered were rejected and undoubtedly a few percent of the ballots never reached their destination.

As for what happens, it depends. If ballots never arrive, arrive too late, or arrive after the election without a postmark, that is almost certainly uncurable (that is, the votes simply won't count). Most if not all jurisdictions give voters the ability to cure an issue with a signature on a ballot by showing up and confirming that the signature is really yours but the window to do so isn't particularly long and the processes to notify the voter are generally not terribly user-friendly. Other issues, like finding boxes of ballots after the election or disputes about whether a particular ballot can be counted despite some defect in filling it out, would likely require a judge to sort out what happens.

Ballots can certainly be lost or delayed in the mail. Ballots can be delivered successfully but rejected because the signature didn't match what the state had on file. Rarely, ballots can also be misplaced. Ballots can also be rejected because of issues with the postmark but presumably not if you're looking to see whether your ballot was accepted prior to election day. And, again presumably not what was being referenced in the quote, there can be issues with a particular ballot that may cause it not to count-- things like voting for multiple candidates, voting for a candidate but then writing in that same candidate, etc. These are the sorts of issues that were at issue in the 2000 Bush v Gore Florida recount. In the most recent New York primary, more than 20% of the ballots that were delivered were rejected and undoubtedly a few percent of the ballots never reached their destination.

As for what happens, it depends. If ballots never arrive, arrive too late, or arrive after the election without a postmark, that is almost certainly uncurable (that is, the votes simply won't count). Most if not all jurisdictions give voters the ability to cure an issue with a signature on a ballot by showing up and confirming that the signature is really yours but the window to do so isn't particularly long and the processes to notify the voter are generally not terribly user-friendly. Other issues, like finding boxes of ballots after the election or disputes about whether a particular ballot can be counted despite some defect in filling it out, would likely require a judge to sort out what happens.