Might it be possible that a a person donate a kidney to any random person?

Yes if good "match": Some very philanthropic people have offered their kidneys to unknown recipients. A chairman of nephrology donated a kidney to a 3rd party, who had a donor who gave their kidney to a 4th party who in turn had a donor who gave a kidney which was used for the nephrologist's wife. Reason being that nephrologist & wife weren't good matches, but all matches within chain were excellent & all did well.