According to Iyun Yaakov, Yosef Lekach, Rashi, and the Vilna Gaon, the advisers were advising Haman to beg Mordechai for forgiveness.
Furthermore, as the Alshich points out, the Talmud (Yevamos 79b) defines Jews as rachmanim, merciful by nature. Therefore, Mordechai would forgive Haman. Having no other choice, Haman would eventually listen (Esther 7:8), and beg Esther for his life.
R’ Moshe ibn Habib is quoted in Dena Pishra as saying that the advisers were suspicious that Esther was Jewish because she decreed that all barbershops were to be closed. Therefore, they advised that Haman beg Achashverosh for forgiveness and revoke the decree against the Jews.
Perhaps they also intended that knowing Esther’s origins – a topic concerning which the king had not yet been satisfied – could be an effective advantage to Haman in having influence on Achashverosh.
The Malbim says the advisers suggested that Haman make Mordechai overconfident with continued honors, so he would stop praying and fasting. They clearly did not know that Mordechai went back to sackcloth and ashes immediately upon his return from the display of honor Mordechai perceived as merely a dog and pony show.
The Malbim explains Haman’s advisers’ words as implying that since Haman started falling already in his degrading display of honor to Mordechai, the natural inertia will cause him to continue to fall.
The Talmud (Megillah 16a) interprets the verse’s double language of “nafol tipol” (“falling you will fall”) by noting that the Jewish people are compared both to the dust, and to stars. The Maharal asks on this Talmudic statement that, historically, every nation has ups and downs. When Babylonia, Greece, Rome, or any other nation sinned, H-Shem caused their civilizations to decline. He answers that the difference for the Jews is that H-Shem directly supervises their ascents and downfalls. Therefore the practical difference is how far up or down.
The Midrash (Bireishis Rabba 8) on Bireishis (1:28) says that man can fall to the lowest depths. There is no middle ground for the Jews; they either fall into the dust or rise to the stars.
R’ Yehonason Eibshutz quotes the Talmud (Brachos 4b) that there is a principle that H-Shem saves the Jews when they are at their lowest. H-Shem waits (kaviyachal, as it were) for the individual Jew or the nation to reach the dust, the lowest point. If a person sitting on the floor falls, that person may fall to the floor. But when one is sitting on the floor and falls, there is not place further to fall. It is at that point that H-Shem must raise that person to the stars.
The Ben Ish Chai writes that the advisers pointed out to Haman that he himself said (Esther 6:11) that the honor received by Mordechai “ye’aseh” (“will be”) in the future tense. He thereby unwittingly cursed himself with Mordechai’s future success.
The Ginzei HaMelech quotes the Ta’amei Esther, who quotes the M’nos HaLevi, who in turn quotes R’ Eliezer of Garmiza that the words nafol tipol are written complete, both with vuvs because Mordechai’s six (the gematria of vuv) actions including fasting, walking through the streets, crying, etc (Esther 4:1) parallel the six (the gematria of vuv) forms of suffering endured by Israel (Esther 4:3). Therefore, Nafol Mordechai and tipol the Jews. The Ginzei HaMelech explains by quoting a Midrash (Vayikra Rabba 34:8) that Moshe accepted upon himself the pain meant for others, and Mordechai did the same. Therefore, paining these kinds of leaders pains all of the Jews. By doing that, Haman is pinning himself against the combined power of the entire Jewish nation.
In a more Kabbalistic explanation, the Rema writes that this falling is actually the second fall, as in the days of Adam (Bireishis 3:15), when the Yeitzer HaRa fell the first time.
The Sha’aris Yosef quotes the Nachal Kedumim that Mordechai was a gilgul, reincarnation, of Yaakov, and Haman was a gilgul of Eisav. One of his proofs for this idea is that the verse (Bireishis 32:12) in which Yaakov prays for Heavenly assistance against Eisav, he says, “hatzileini na miyad” (“save me please from the hand”), which have initial letters that spell out Haman. Although Yaakov never physically fought Eisav, he did fight Eisav’s guardian angel. The verses describing this exchange (Bireishis 32:25-30) never explicitly names the victor, which prompts the Midrash (Bireishis Rabba 77:3) to state that it would remain unclear who won except for the fact Eisav’s guardian angel had to go back and forth several times. Just as Eisav’s angel had to go back down, Haman’s advisers here are implying that, being a gilgul, Haman would similarly fall twice before Mordechai.
The Maharal notes that Haman’s advisers must have known that Mordechai was a Jew, as Haman, himself mentioned to them (Esther 5:13). After all, it was possible that Mordechai was brought into Persia with King Yechanya (Esther 2:6), but was not actually a Jew. Therefore, the Talmud (Megillah 16a) understands the advisers’ remarks as relating to Mordechai’s tribal lineage. In effect, they were saying that if he were from the tribe of Yehudah, Binyamin, Efrayim, or Menasheh, Haman could not expect to be successful against him. In Bireishis (49:8), Yaakov promised Yehudah that his descendants would conquer their enemies. In Tehillim (80:3), King David prays that H-Shem strengthen Efrayim, Binyamin, and Menasheh. As it happens, Mordechai could trace his paternal lineage to one of these listed tribes and his maternal lineage to another.
The Maharal points out that Yehudah, Efrayim and Binyamin all represent Jewish unity because the Beis HaMikdash, and the Mishkan in Shilo and Nov were all located in their tribal inheritance. As proof, the Maharal quotes from the verse (Bamidbar 16:6) in which Moshe attempts to quell the rebellion of Korach and his group by saying they should all bring fire-pans. The entire group bringing individual fire-pans would represent the very opposite of unity. In fact, the unity of Jews’ uniqueness with H-Shem’s Uniqueness fights off the doubts and confusion that Amalek represents. The Midrash (Esther Rabbah 6:2) considers the description “Yehudi” as being derived from the adjective “yechidi” (“unique”) or the noun echad, (“one”).
According to the Targum, the advisers were not asking if Mordechai was a Jew, but if he were from the holier, saintly Jews. The Vilna Gaon writes that, unlike Haman’s assertion that the events he described were chance, Zeresh and the advisers were saying that it was not. After all, as a member of the Yehudim, Mordechai enjoyed the situation promised by the Talmud (Shabbos 156a, Nedarim 32a) that “ein mazal b’Yisroel” (“there is not mazal for Israel”).
R’ Dovid Feinstein explains that the advisers were focusing on the fact that Haman’s situation could go either way, based on Jews’ behavior.
The Ginzei HaMelech quotes R’ Meir Shapiro, who focused on the word, “zerah” (“seed”). They were saying that if the Jewish youth had no serious connection to Mordechai. They considered the aged Mordechai only powerful if he still held relevant sway on the youth of his people. So when Haman told them that Mordechai was surrounded by thousands of students learning a (temporarily) outmoded law regarding grains and Temple service, the advisers realized Haman has no chance. When Judaism is relevant for the invigorated youth, our enemies stand no chance.
Similarly, says the Ginzei HaMelech, Mordechai has to be mizerah (“from the seed”) of Yehudim – an invigorated member of the youth in vitality – and then Haman should just give up.
According to the Ben Ish Chai, Haman gave a short history lesson saying Mordechai was a descendant of Shaul, who only ruled briefly and not successfully. In response, the advisers said, that may be true, but Mordechai was also a descendant of Yehudah from his mother’s side, so he will win as promised. Homiletically, he reads the word im (if) as eim (mother).
Rav Galico writes that the verse calls Haman’s advisers wise because these were those of his friends who were wise.
The M’nos HaLevi say they were wise due to the straight talk they provide. Therefore, the verse calls them “wise” instead of “loved ones.”
According to the Talmud (Megillah 16a), anyone who says something wise, whether Jew or gentile, is called wise. After all, the Talmud (Megillah 6b) admits that there is wisdom among the gentile nations.
R’ Shlomo Kluger says they were wise because they saw that all of these events Haman described did not just happen, but occurred due to the snowball effect that have built up over many years – perhaps since the time of Amalek.
R’ Mendel Weinbach says they are wise because all wisdom can come from the Torah. The Vilna Gaon, for instance, could purportedly give entire discourses on calculus without ever having seen a textbook on the subject.
Rav Avraham Chadida writes that these advisers knew that when things are out of their expected order are a sign that something good is about to occur. He gives the example of Rivka’s wonder at her unusual pains in pregnancy (Bireishis 25:22), Moshe’s curiosity at the burning bush (Shemos 3:2-3), and even cold weather in the middle of a summer.
Shar bas Rabim notes that the Talmud (Tamid 32a) defines a wise person as “haro’eh es hanolad,” or someone who can predict future events by logically observing history. Actually, these advisers were indeed correct!