Earlier quoted context omitted.
Are you saying, "prove it has happened" or "prove it is a risk"? I doubt it's happened yet, but I think the risk is getting worse every year (technology enables this, like when personal identifying information on large numbers of American voters leak from large companies...)
How exactly will you use this PII to perpetuate voter fraud? Show up at a polling station with fake ID or PII? Then at another polling station with another piece of fake ID or PII? What's your plan for voting staff checking the records, and finding out that 'you' already cast a ballot at that station? This kind of fraud is incredibly risky, and does not scale (And is trivial to combat). Election fraud by the process…
Generally, you register to vote. As long as you input plausible information and a real address you can receive mail at, you are likely to get on the rolls. Once you get on the rolls, you just show up at the polling station and tell them who you are (no ID required), they look for the name in the book, mark you as having voted, and you go vote.
Several years ago they did pass a law federally requiring an ID if you couldn't provide the last-four of an SSN or a driver's license, though, if you're a new voter. Not sure how that works if e.g., you're Amish and don't have an SSN or driver's license.