Let’s start with the carriage of a singing body as it relates to classical music: art song, operetta and opera. Is these genres there can never be stiffness, but there must always be a calm poise, prepared to respond physically to the emotion of the music.
Many are asked to do things: keep your shoulders back, keep your chest high; some asked to keep the chin low, others high. One of my favorites is “pinch the buttocks for high notes”. Another and far more common is: draw in the lower abdominals to support the tone, especially for high notes.
No part of you should be held in any way, drawn in, pushed out, lifted up or pressed down when you are singing. Your conscious sense of physical action will not be accurate and will usually overdo the effort, resulting in dangerous tension. The only things that you hold in any way when you sing are your breath as you imagine swimming under water, and the flow of words.