Revealing my ignorance of food here... but how long does ham stay good for? That's the ham their father sent them back in chapter 1, isn't it? I mean... sure, almost anything can last forever if you freeze it, but wouldn't that eventually affect the quality?
It's covered in salt to draw out moisture and preserve. Then its dried. Lasts several months after you first start cutting into it as long as you cover the part you've cut with some of the rind or a cloth. Also you want it at room temp in a dry area. Not in the fridge.