I am quite sure that it 1. doesn't have a name, and 2. is obsolete.
I read of this technique in a book on traditional English cooking (turns out that it was very similar to French cooking some centuries ago). Back then, meat was always roasted over an open fire. The fire is a hot and uneven source of heat, and they always had huge pieces of meat in a castle kitchen, so it was normal for the inside of the roast to be underdone, while the outside was practically ruined. So they used the good and tried technique of wrapping the roast, cooking for longer time than it would have been possible with unwrapped meat (which helped the raw core), then discarding the ruined wrapper. As the most plentiful ingredient in a noble's kitchen used to be meat (at least in England - maybe the French got the recipe for them despite the better availability of vegetables?) it was just a convenient tool to do the job.
Nowadays, we don't need to do this. A modern oven roasts much better. There are other, cheaper wrapper materials available for whoever wants to use one. I guess that some chefs may be reviving it because it sounds so unusual, it is guaranteed to attract attention. It could be worth eating, but frankly, if I wanted to know how pheasant cooked together with veal tastes, I would choose a recipe which doesn't discard the veal.
As for the name: The book I am referring to ("The cookery of England" by Elisabeth Ayrton) is based on very good research. The author publishes medieval recipes from manuscripts verbatim, etc. She also explains many points, gives some historical background, etc. I am 99% sure that if there was a special name for this technique, she would have known it and mentioned it at the point she describes the practice. For example, she explains "frothing" (pouring batter over the almost cooked joint) in the same paragraph she referrs to wrapping.
Traditionally, snails are removed from the shell and simmered for an hour or so in stock or bouillon. Then they are placed back in the shell with a little of the stock, and the shell is 'sealed' with butter, which is usually flavoured with garlic, parsley and shallots.
They are then roasted in a hot oven until the butter has just melted.
Best Answer
Rillette is pork cooked in fat (not really confit, but close to).
Most of what I've seen on the internets is that you can freeze the rillette for longer storage; if not, keep at most for 30 days in the fridge.
You can pour a little bit of the fat on top of the rillette in the container, mostly for extra flavour, not for long term conservation.
I don't know enough about pink salt (Himalayan salt or the Pink curing salt ?) to help you there.