If only members of one party are running in an election, so the primary will decide the race, the primary is open to all voters. But if any other candidate files, including a write-in, the primary is “closed,” meaning only those registered to the party can vote, even though write-ins don’t pay filing fees and don’t appear on the ballot.
It’s common for candidates who believe they’ll have an advantage in a closed primary to encourage a political ally or friend to file as a write-in.
Both Valion and Vazquez denied that anyone asked them to run to keep the primaries closed.