Kind of a weird question and trust me, it has no application in my life:
What if I had a young pig, for example, and made a cast-iron “shell” that fit the pig perfectly and then put it inside the shell and then kept feeding the pig? (Consider that maybe the pig’s head is outside of the shell.)
In simpler terms, what happens when something like a pig tries to grow in a space where there is no more room to grow?
At first I thought this was a thread about Pig Iron.
It would die a long drawn-out death from suffocation; unless it died sooner of tetanus, gangrene, or just stopped eating when things got tight and starved itself to death.
I was expecting something about corn bread.
Cast iron is too heavy to be practicable. OP should take up bonsai kittening.
You can get a rough idea from articles about chinese foot-binding. Every so often there’s a horrendous story about animal neglect where a dog for example, never has a collar removed ait it grows around it.
But as TrueCelt points out, the thing has to breath and gradual tightening would eventually suffocate it.
I think it might be a race between suffocation and infected pressure sores - if it can’t move, then it can’t relieve pressure on whatever parts of its body happen to be chafing or pressing against the container - it can’t move to restore constricted circulation, etc.
I thought it was a thread about a cast iron bacon press in the shape of a pig.
The most immediate cause of death will by hyper/hypothermia. With all heat exchange being forced to go through the shell, the animal will die from overheating, unless the external temperatures are very, very cold, in which case it will die of cold.
If you somehow manage to control for temperature, with absolutely no ability to move its limbs thromobosis will kill the animal within a few days at the latest. Whether it actually dies from embolism, necrosis or loss of clotting factor caused by the thrombosis is all that remains uncertain.
If you magically arrange for the animal not to die of hyperthermia or thrombosis then, depending on the age of the pig and how much it would actually eat under such stressful conditions, suffocation could kill it within days, but more likely a couple of weeks.
Pressure sores will probably kill it wihtin weeks, months at the latest.
Why a pig shaped tourture chamber for the little squeker? Why not put him in a square shaped box and make a square shaped piggy? You know, like those square Japanese watermellons I once read about! There could be a market for square lap pigs!
But if you try to later put it in a round shell you’ll have a problem, because you know what they say about trying to fit square pigs.
Think about doing that to a baby. Do you really expect it to survive long?
You can avoid pressure sores by using a fluffy animal, to provide its own cushioning. Here, for instance, are the Bonsai kittens we’ve all heard about.
And for the hell of it, here’s Pig-Iron.
I thought it was going to be a thread regarding Hollywood stars and their relation to the steel industry. (Too far a reach?)
More than once, even.
I can’t decide which example was funnier (sillier?), the one from astro’s “Space Trucker” or Max Torque’s. 
(After an informal survey, Max Torque wins, 4-1.)