A common concern about vote-by-mail in the United States is that mail-in ballots are sent to dead people, stolen by bad actors, and counted as fraudulent votes. Studying Washington state's vote-by-mail program, we link counted ballots and administrative death records to estimate the rate at which dead people's mail-in ballots are improperly counted as valid votes, using birth dates from online obituaries to address false positives. Among roughly 4.5 million distinct voters in Washington state (2011-2018), we estimate that there are 14 deceased individuals whose ballots might have been cast suspiciously long after their death, representing 0.0003% of voters. Even these few cases may reflect two individuals with the same name and birth date, or clerical errors, rather than fraud. After exploring the robustness of our findings to weaker conditions for name-matching and the inclusion of deaths closer to Election Day, we conclude that counting dead people's ballots as votes seems extraordinarily rare in Washington's universal vote-by-mail system.