Learn Finnish: Mun ois pakko lähettää osoitteenmuutos viimetipassa. - I would have to send the change of address at the last minute.

This is the core rule of the nominal necessity construction you are learning. When you use a necessity phrase like on pakko (or here, ois pakko) followed by a 1st infinitive verb (lähettää), the object drops its normal accusative -n ending and stays in the basic nominative case.

Wait, the first half of osoitteenmuutos is in the genitive (osoitteen-). Does that break the object rule?

Not at all! The rule applies to the final, main part of the compound word, which is muutos (change) — and that is correctly in the nominative here. The first part (osoitteen) is just a built-in genitive modifier indicating what is being changed (a change of address).

Why does the sentence use ois instead of on?

ois is a very common spoken-language form of olisi, which is the conditional ("would be") of olla. Using the conditional softens the necessity, changing "I have to" (mun on pakko) into "I would have to" (mun ois pakko).

Just as a refresher, why is the subject mun instead of mä?