I assumed that to vote from abroad, overseas voters must also have a current address or own property in the US.
There is no requirement to own property or have a current address in the US to vote from abroad.
It's head-scratching to think that such a fabricated story as this one still circulates amidst the U.S. overseas citizen communities around the world. Do we not remember that even many Americans living in the U.S. domestically do not own property or have a fixed mailing address?
But the reason this myth has not been stamped out once and for all is because it stems from the "idea" that absentee voters must receive their ballots somehow -- so maybe they are sent to our old address in the U.S. Of course, that would be ludicrous, as you, the voter, are not living there. Overseas ballots are sent to you at your location abroad, or online, per your request.
This myth is compounded by the fact that, as an overseas voter, when you register and request your ballot, you do indeed enter your last U.S. residence address. That is the address that is considered your Voting Residence Address - or, in other words, your address for voting purposes. Your Voting Residence Address is in a particular election jurisdiction. Its location determines your voting district and the election office that will receive your request for an overseas ballot, send you the ballot and count it when received.
See more on Determining Your Voting Residence Address in our Overseas Voting Explainer.