I don’t think any state allows you to register and vote without ANY type of check as to residency. Many do not require an official picture ID, but do require something like a utility bill, or you register and they send you a voter’s card. The secretary of state or registrar has a check system. Even the homeless population has some type of system to show that they live in the precinct and have for at least 30 days before the election. Many register at a shelter or church and use that as an address, and the registrar can confirm that church or shelter is the ‘address’ of the voter.
Here, if you vote absentee, you have to make a copy of your ID to include with your ballot, and have to sign the envelope after it is sealed. The absentee ballots are linked to a local address even if sent to an OOS one. Many absentee ballots are voided because the voter doesn’t follow the directions and the clerk can’t confirm that the vote is by a resident.