This is one of the most important topics to cover because the misconception on how exactly one sings mezza voce and pianissimi has destroyed or limited many voices. In addition to how these skills are done correctly are also the incorrect ideas on when one is ready to do them and what it means if a singer cannot do them - especially early on in their training and/or if they have a big voice.
Let me first start by explaining how one actually sings mezza voci and pianissimi correctly. Basically, the more chest/lower register one sings with the more the thyroarytenoid muscles are engaged. The less TA is engaged the more towards mezza voci and pianissimi one sings; or the more towards the falsetto one sings. The TA no longer dominates in production, but rather the cricothyroids become dominant; as well as other muscles that need to engage. Therefore, it is important that one have a strong falsetto and chest register so as to easily move more towards one or the other.
The mistake in trying to sing mezza voci and pianissimi is to start to close the throat to diminish the sound. This leads to the closing muscles of the throat becoming very strong. When that happens it becomes more and more difficult to open the throat. And it can cause many different issues such as a wobble. This is exactly what happened to Maria Callas.