Chabad.org — English translation + Rashi
Torah Temimah (Pesachim 93a): those who do the second include shogegin, anusin, mezidin, tamei, and one who was on a distant road.
English: The Sages taught: these are they who offer the second: zavim and zavot, metzoraim and metzoraot, [niddot] and those who had relations with niddot and women who gave birth, the shogegin and the anusin and the mezidin, and one who is tamei and one who was on a distant road.
Status-change and barrier cases — the second month catches those who only became able or obligated after the first had passed.
The Torah anticipates people whose legal capacity or purity status changes mid-season.