They check citizenship before adding the name to the voter roll.
What makes you think that?
What state are you living in? In what alternate universe?
In many states they don't check. You fill out the form, send it in, and that's that. The fine print says claimed "under penalty of perjury" (that's never applied)" that you're a citizen. No I.D. required.
This is especially since the federal "motor-voter law" requires sates to provide (piles of) mail-in voter registration at many places people otherwise interact with the government, including the places they get their drivers licenses. Grab a handfull of 'em - or ask for a couple boxes. "We're running a voter registration drive." Perfectly legal. What you do with them afterward is a separate issue. (That's how ACORN - for which Obama once worked - ran voter registration drives among immigrants - illegal and freshly arrived - (using federal funding), and eventually got dropped by the Fed when some of their people just started making up obviously fake names and got caught.)
Or register (sometimes on voting day) at the polls. Commute from polling place to polling place on election day. (Your party will often provide convenient transport for you...)
My wife encountered one "undocumented immigrant" on our block who proudly showed her his more-than-twenty voting cards. When told that was illegal he said that if the officials thought it was important they'd be doing something about it.
The registrars of voters don't have the time, manpower, budget, (and often claim not to have the authority), to check all those applications. If they're Democrat appointees, they don't have the will, either: Those phantom votes are probably for their side. If they're Republican appointees, they're subject to lawsuits for "voter intimidation" if they try to actually purge ineligible voters from the rolls.
Once a voter is on the rolls, just TRY to get them off. We've had someone who never lived at our address voting absentee for years now. He was still doing so as of the last election. We get his election materials. We've tried to get him removed but the registrar won't do it. We've tried to find out where the absentee ballots are sent but they refuse to tell us: "He might be a policeman or a stalking victim..."
Our former next-door neighbor died when her second liver transplant was rejected. Her daughter reported her death to the registrar - repeatedly. Even took the death certificate to the registrar's office. She was taken off - repeatedly - and repeatedly put back on. Finally they refused to take her off, because she was still voting by mail. (I'd LOVE to know how the post office delivers the ballots and gets her votes returned, or at least how to address mail properly to reach "the other side". I have a number of deceased friends and family members with whom I'd like to correspond. B-b )
That's about twenty five fake votes that we personally KNOW about in ONE BLOCK of ONE TOWN. Most of them by ONE illegal immigrant whose citizenship obviously wasn't checked - repeatedly.
Now combine motor-voter with automatic absentee voting upon request (sometimes a check box on the original registration form). With a few (or even one) mailing addresses you can create phantom voters as fast as you can make up names and fill out one or two forms apiece, for the cost of a couple stamps. There was only a minor news blip, and no prosecutions, when it was discovered that several thousand "absentee voters" were having their ballots delivered to the same address in Berkeley.
So don't tell me "voter fraud is nearly non-existent". We have plenty of existence proofs. What we lack is substantial effort, on the part of officials (who have an interest in maintaining the status quo, which includes them being in power) to measure its extent or cure the problem