Like everything in singing, there are many ways to look at breath function. 1) The periodic propagation of air is what we hear as pitch (I.e. in singing, breath is released by little puffs hundreds of times every second. This rapid machine-gun-like release is pitch). 2) The uninterrupted pressure of air underneath the vocal folds that makes for continuous sound.
The mechanism is simple. The lungs serve as a full bag of air that is squeezed by the rise of the diaphragm and the contraction of the many abdominal muscles that reduce the volume of the ribcage further squeezing air toward the vocal folds (hopefully). If the lungs are not completely filled, when the diaphragm and abs compress the air, instead of providing steady pressure underneath the folds, the pressure first fills the empty part of the lungs. Without adequate pressure to create the desired tone, the folds will automatically squeeze together to increase pressure. This is called pressed voice.
In a healthy voice. The vocal folds close fully over lungs and trachea full of air. This provides the means for pressure on one side. The diaphragm and abs work to pressurize from below. The abs and diaphragm work automatically.
Therefore in terms of breath support, the singer’s responsibility consists of 1) taking a full breath to fill the lungs to capacity and maintain the state of expansion 2) produce a balanced onset whereby the folds gently but fully close for every vibratory cycle hundreds of times per second. The diaphragm and abs are activated automatically by the brain to provide the necessary pressure depending on the desired sound. These automatic actions provide sensory feedback in the pelvis via the Rectus Abdominus muscle in around the abdomen through the many abdominal muscles. These sensations are automatic if the singer accomplishes 1 and 2. If the singer feels a need to actively control the abs , it is a sign that 1 and/or 2 has/have not been accomplished. It is crucial that the singer takes charge of what s/he is responsible for and not what should be automatic.