Learn Italian: Il medico mi ha assicurato che la febbre sarebbe passata. - The doctor assured me that the fever would pass.

This is the 'future in the past' structure. The doctor made the assurance in the past (ha assicurato), and the fever passing was going to happen after that. English uses 'would' plus a verb to show this, but Italian requires the past conditional to show a future action from a past perspective.

Why does passare use essere (sarebbe) here instead of avere (avrebbe)?

When passare is used to mean an illness ending or time going by, it takes the auxiliary verb essere. It only takes avere when there is a direct object, like passing an object to someone or spending time (ho passato il fine settimana).

Since we use essere for the past conditional here, does the ending of passata matter?

Yes! Whenever a compound tense uses essere as the auxiliary, the past participle must agree in gender and number with the subject. The subject is la febbre, which is feminine singular, so the participle must end in -a (passata).

Why doesn't assicurato change its ending to agree with mi?