1) A NAZIR WHO BECOMES "TAMEI" WITH "TUM'AS HA'TEHOM"
QUESTION: The Mishnah teaches that a Nazir is not obligated to shave for Tum'as ha'Tehom. This means that if a Nazir completed his Nezirus and then discovered that while he was a Nazir he became Tamei from a k'Zayis of a Mes that was hidden somewhere, never seen by a human eye, the Tum'ah is ignored. However, the Mishnah adds that a condition is necessary in order to ignore the Tum'ah. If the hidden Tum'ah was buried underneath a water-filled ditch and the Nazir immersed in the water to become Tahor from Tum'as Mes, the Tum'as ha'Tehom is not ignored and he remains Tamei, since he had a Chezkas Tamei (he was Tamei until that point). Only when the Nazir was Tahor and immersed in the water for another purpose is the Tum'as ha'Tehom ignored.
Why does the Mishnah state that Tum'as ha'Tehom is not Tahor when the Nazir was Tamei with Tum'as Mes at the time he immersed in the water? Even if he was Tamei with Tum'as Sheretz, he has a Chezkas Tamei and the Tum'as ha'Tehom should prevent him from becoming Tahor!
(a) The simple answer is that the Nazir's Chezkas Tamei affects him only if he was Tamei with the same type of Tum'ah as the Tum'as ha'Tehom (i.e. Tum'as Mes). If he was Tamei with a different type of Tum'ah, such as Tum'as Sheretz, the Chezkas Tamei cannot make him acquire a different Tum'ah, that of Tum'as ha'Tehom (Tum'as Mes).
(b) However, REBBI AKIVA EIGER suggests a different explanation for the Mishnah. The Gemara later (64b) says that if the Nazir Tamei -- on the seventh day of his Tum'ah, after his Tiglachas but before sunset of that day -- comes across Tum'as ha'Tehom, he is not considered to have a Chezkas Tamei, because "sunset occurs by itself" and he lacks nothing to make him Tahor. TOSFOS (DH Amar Abaye), the ROSH, and RABEINU AZRIEL (cited by the SHITAH MEKUBETZES) add that Tevilah in a Mikvah (when no Tiglachas is needed) is also not considered something which the person lacks in order to become Tahor, because the Mikvah is in front of him and he has the ability ("b'Yado") to immerse himself. The only way a Nazir can have a Chezkas Tamei is if he lacks his Tiglachas. A Nazir who did not yet have his Tiglachas of the seventh day he is considered to have a Chezkas Tamei.
Rebbi Akiva Eiger suggests that if the Nazir is Tamei only with Tum'as Sheretz, he does not need to shave and thus he is not considered lacking anything in order to become Tahor (all he needs to do is immerse in a Mikvah and wait for sunset, which are considered insignificant actions which he does not lack). This is why Tum'as Sheretz does not give the Nazir a Chezkas Tamei to make him Tamei with Tum'as ha'Tehom.
Rebbi Akiva Eiger points out that there is an important practical difference between these two explanations. What is the Halachah in the case of a Nazir who immersed in water over a Tum'as ha'Tehom in order to become Tahor from the Tum'ah of Revi'is Dam or of Rova Kav Atzamos? Although these Tum'os are the same type of Tum'ah (i.e. Tum'as Mes) that comes from k'Zayis of a Mes, nevertheless a Nazir who becomes Tamei from a Revi'is Dam or from a Rova Kav Atzamos does not need to shave (54a). According to the first explanation, the Nazir should have a Chezkas Tamei since his Tum'ah is the same type of Tum'ah as Tum'as ha'Tehom. In contrast, according to the second explanation (that only the lack of Tiglachas gives the Nazir a Chezkas Tamei), the Nazir (who became Tamei from a Revi'is Dam or from a Rova Kav Atzamos) should be Tahor from Tum'as ha'Tehom since he does not have a Chezkas Tamei.
(See ME'IRI, who explicitly states that the Nazir is considered b'Chezkas Tamei only if he has the type of Tum'ah which is "Soser" his Nezirus. This implies that he follows Rebbi Akiva Eiger's second explanation, that it is only the lack of Tiglachas which gives the Nazir a Chezkas Tamei.)