Stale bread is soaked and squeezed before it goes into a mixture because it does 2 things: it holds the liquid released by meat and vegetables as they cook, and it keeps the mixture from drying out. If added dry, it draws this liquid from the mixture itself and the meatball comes out dry; if added without squeezing, it releases too much water into the mixture and makes it runny. Judge the right consistency by hand, not by weight.
Bread crumb is a porous sponge made of cooked starch and gluten. When added to the mixture, it spreads among the ground meat or rice and creates a small reservoir of moisture around each grain. As meat cooks, its fibers contract and squeeze out their juices; the bread in the mixture holds onto this liquid, keeping it inside instead of letting it run out of the meatball and evaporate in the pan. What makes the meatball come out tender and juicy is these small reservoirs more than the meat itself. If you cut the cooked meatball in 2 and see liquid glistening inside, these reservoirs have done their job.
Stale bread is preferred because of its texture. Fresh bread crumb is moist and turns into dough when soaked; it stays in clumps in the mixture and becomes gummy when kneaded. The starch in stale bread has firmed up, so the bread absorbs liquid, breaks apart, and crumbles in your hand. Crumbled stale bread spreads evenly through the mixture, while fresh bread gathers in one spot. How stale it is also matters: bread that has dried out and hardened absorbs water slowly, so it needs a slightly longer soak. Use only the inside of sliced bread; the crust does not soften in the mixture and feels hard when you bite into it.
Soaking plumps the bread, while squeezing removes the excess. Bread left in water absorbs much more than it can hold; if that excess is not squeezed out, it goes into the mixture and loosens it. A loose mixture will not hold its shape, meatballs spread in the pan, and stuffed-vegetable filling leaks through the leaves. That is why the bread is pressed and squeezed in your palm, continuing until water stops dripping. Properly squeezed bread stays moist but not wet, as a ball that crumbles easily when pressed with a finger. Discard the squeezed-out water; do not add it back to the mixture.
The opposite is also a mistake. If bread is added to the mixture dry, as dry crumbs without soaking, it draws water from the mixture itself. Then there is no room left to hold the liquid the meat will release as it cooks, because that space has already been filled; even if the outside of the meatball browns, the inside comes out dry and firm. That is why breadcrumbs are moistened first with a few spoonfuls of liquid instead of being added directly to the mixture. The soaking liquid can be water or milk; bread soaked in milk gives the mixture a softer texture.
You can tell by hand whether the mixture is right. Take a piece of the mixture with bread kneaded into it and squeeze it in your palm; if your fingerprints remain on the surface and the piece holds together without falling apart, the consistency is right. If the piece sticks to your hand and squeezes out between your fingers, the bread was not squeezed well enough; add a little more dry bread or breadcrumbs. If the piece cracks and crumbles, the mixture is dry; knead it again with a little water. A gram measurement does not help here: the bread’s moisture and staleness vary every time, so your hand is the measure.