A leap year in the Jewish calendar is a year containing two months of Adar, to which we refer as "Adar Rishon" ("the first Adar") and "Adar Sheni" ("the second Adar").
If a person passes away, Heaven forbid, during the month of Adar Rishon in a leap year, then his Yartzeit (anniversary of his death) is observed on non-leap years on the corresponding day in the month of Adar. The exception to this rule, as Rav David Yosef (son of Hacham Ovadia Yosef) writes in his work Torat Ha'mo'adim (laws of Adar, p. 19), is when the individual passed away on the thirtieth day of Adar Rishon. The thirtieth of Adar Rishon is observed as the first day of Rosh Hodesh Adar Sheni, and therefore on non-leap years, the Yartzeit is likewise observed on the first day of Rosh Hodesh Adar the thirtieth of Shevat. Even though the person died on the thirtieth of Adar Rishon, in determining the Yartzeit we focus on this day's status as the first day of Rosh Hodesh Adar Sheni, and thus the Yartzeit will be observed on the thirtieth day of Shevat, or the first day of Rosh Hodesh Adar.
Of course, this applies only on non-leap years. On leap years, the family members will observe the Yartzeit on the actual date on which the individual passed away the thirtieth of Adar Rishon.
