Let me add to your confusion. Some places/states allow illegals to have driver's licenses. With said driver's license, couldn't they just use the motor/voter law to get registered to vote and then do so? In addition to being counted for the census, they could have the ability to "count" in elections.
Only because of "processing errors"
Or simple confusion about the system...
There was reporting by mainline news orgs. NBC, Fort Worth Star-Telegram, Dallas Morning News, that said Texas officials had found a significant number of people registered that shouldn't be. Then it was reported that those reports were just mistakes and threats of litigation from civil rights groups apparently stopped efforts to investigate or continue the "state’s recommended procedure for verifying voters’ citizenship status"...
There was also a lawsuit in Penn. over the issue of non citizens being registered but when a settlement was finally reached there was no mention of non citizens only the state cleaning up it's rolls by removing dead people.