The Mishnah in Nazir 6:3 states:
סְתָם נְזִירוּת שְׁלשִׁים יוֹם. גִּלַּח אוֹ שֶׁגִּלְּחוּהוּ לִסְטִים, סוֹתֵר שְׁלשִׁים יוֹם. נָזִיר שֶׁגִּלַּח בֵּין בְּזוּג בֵּין בְּתַעַר אוֹ שֶׁסִּפְסֵף כָּל שֶׁהוּא, חַיָּב. נָזִיר חוֹפֵף וּמְפַסְפֵּס, אֲבָל לֹא סוֹרֵק. רַבִּי יִשְׁמָעֵאל אוֹמֵר, לֹא יָחוֹף בַּאֲדָמָה, מִפְּנֵי שֶׁמַּשֶּׁרֶת אֶת הַשֵּׂעָר:
A basic nazir [vow] is [for] thirty days. If he shaved or bandits shaved him it voids the thirty days. A nazir who shaved, whether with scissors, with a razor, or if he trimmed at all, is liable. A nazir can rub and trim but not comb. Rabbi Yishmael says: "He should not rub with earth, since it tears out the hair."
Suppose a Nazir does an action that indirectly causes his hair to be removed (for example, he undergoes chemotherapy and his hair falls out). Does doing that action void his Nezirus counting? Does the Issur of a Nazir shaving his head apply to indirect manners of hair removal?
On the one hand, the Mishnah seems to say that both Oneis (unavoidable action) and Psik Reisha (guaranteed outcome) are forbidden. That would seem to correlate accrately to this scenario.
On the other hand, perhaps other factors such as Davar She'eino Miskavein (unintentional result), not removing the hairs in a 'normal' manner, etc. would make this case not a violation of Nezirus.