In the 2020 United States Presidential Election in Dixville Notch, New Hampshire, Joe Biden received 5 votes and Donald Trump received 0 votes. Biden received 100% of votes cast.
In the 2016 United States Presidential Election in Kalawao, Hawaii, Hillary Clinton received 14 votes, Jill Stein 5, and Donald Trump 1 vote. Trump almost received 0% of votes cast.
There are probably rural places where the result is reversed and the Republican candidate may get 100% of the vote.
Apparently, Gir Forest in India had exactly one voter.
In the 2013 Falkland Islands sovereignty referendum, only 3 people voted No.
When at least two or three votes are cast for an alternative there is still somehow a secret ballot, but when 100% votes for a single alternative, the principle of the secret ballot is violated. The secret ballot is guaranteed by the Universal Declaration of Human Rights, Article 21.3 (emphasis mine):
The will of the people shall be the basis of the authority of government; this will shall be expressed in periodic and genuine elections which shall be by universal and equal suffrage and shall be held by secret vote or by equivalent free voting procedures.
(since this declaration is universal, it applies worldwide, including in the United States; moreover, the United States voted in favour of this declaration in the United Nations and was leading in drafting the text in the first place, so arguably it should apply in the United States; however, I don't know if it's actually a law)
Are there any systems or proposals for systems to mitigate this problem? I could imagine either a rule that voting precincts must have a minimum size (in the extreme case of a precinct with one voter, their vote could never be secret), or where any precincts with 100% for any candidate must be grouped after the election with others such that the result is less than 100% (effectively merging precincts after the election; voters could still verify the combined result but not the individual result per precinct, but secrecy were maintained).
(the counterpart, preventing any results where a candidate receives 0%, is probably not feasible, due to obscure candidates who may receive less than 0.01% of the vote nationwide, and thus 0 votes in many precincts; but with larger precincts, the nationally winning candidate getting 0% of the vote should be unlikely)