The beginning of a note after a breath is called an “onset” or an “attack”. The way a note ends at the end of a phrase, before a new breath is taken, is called an “offset” or a “release”. If the phrase begins and ends with a vowel, you have a good laboratory in which to play with how the sung sound starts and stops. You can do this by just singing a phrase from a song on any vowel, or with a vocalise on “Alleluia” or a sentence such as “Ann tuned her oboe”, etc. I like simply singing an /a/ (as in father) for working with these elements.
It can be informative to consciously not move any air before starting a phrase. Right before the singing sound starts, just suspend the air for a second or two, with the throat and lower regions neutral, neither inhaling nor exhaling. You can do this after inhaling, or without inhaling at all. Similarly, at the end of a phrase, you can suspend the breathing process before doing anything else to check in with the body and to play with expressive options.
Suspending at the beginning of phrase can give a window into these questions: What feels active? What feels relaxed? Is my throat open, closed, or neither? After the suspension, what happens if I ___ before I begin the sung sound?
Suspending the process at the end of a phrase offers similar options, but can be even more impactful to the artistic result. In a discussion online, some folks insisted that all releases should be silent and result in a recoil that brings in new breath. But, golly, there is so much more you can do with it! For example, I recall a time when I sang Jaime León’s Rima in a recital. At the end of the song, I suspended the release and just let the phrase hang there dramatically and visually, with no inhalation until the short postlude was over. The text was “No puedo decirte” (“I cannot tell you”). Pleasant gasps came from the audience before the applause. It was a magic moment.
Listen to some of the great tenors, such as Caruso, and you will hear some quite noisy releases, which add a powerful dramatic element in the right repertoire. There are plenty of dramatic moments in opera, musical theatre, and every genre of song, especially at lyric “commas”, where an audible inhale or exhale is not only acceptable, but an exciting addition.
If the singer is not capable of virtually silent breaths, that is a problem. It indicates interference in how the singer is breathing, and can make phrases that should be relatively peaceful or mellow sound ridiculous. However, breathing noiselessly all the time runs the risk of a performance that isn’t as exciting as it could be. Listening to the breathing patterns in animated speech can give clues as to how breathing for singing can be varied. Try playing with the suspended breath, then when you are not suspending anymore, you can treat onsets and releases with more intention, according to what you are expressing.