You could use a SSN from a person residing in another state. Or, according to this form: https://www.eac.gov/sites/default/files/eac_assets/1/6/Feder..., "If you do not have a current and valid driver license or non‑operating identification license or a social security number, please write “NONE” on the form. A unique identifying number will be assigned by the Secretary of State."
I'm guessing there isn't much verification, as I've heard of immigrants accidentally being registered to vote because they checked "Yes - I'm a US citizen" on a driver's license form.
You cannot see how they voted, but you can see that they voted.
This is how all political campaigns know which people always vote, which people usually vote, which people sometimes vote, and which people never vote.
For example, in Washington State there is a voter registration database. These are public records that can be requested from the state (https://www.sos.wa.gov/elections/vrdb/default.aspx). In them, the date that the person last voted is listed (see "lastVoted" in column 36 https://www.sos.wa.gov/_assets/elections/vrdbdatabasefields....).
In addition, King County ballots come with a unique identifying code that you can look up on their website to see if your ballot was received or counted (https://info.kingcounty.gov/kcelections/vote/myvoterinfo.asp...).
Most common is allowing the inspection of the list of absentee requestors, like in North Carolina: The chief election judge of each precinct is required to post one copy of the precinct absentee ballot list “in a conspicuous location in the voting place.”
That said, there are other states that do not allow this, so it's less widespread than I originally thought, and when it is allowed, it's usually either just the absentee requestors, or the list is made available after the election, not during. Sorry.
-Generate fictional registered voters at real addresses
-Elections office dutifully sends out ballots
-Rely on actual residents to toss those ballots. Or maybe they vote with them - if it's in the right district, they're likely to vote for the right person anyway
-Send in copies of their mail-in ballots come election time
This would work if you keep the numbers low. And the numbers of dead/moved voters would help camouflage it.