Liquefying through long boiling

I don't think that the word exists at all. "Overboiling" and "overcooking" always implies an undesirable result. Else, you have to exactly describe what you are doing, which depends on the dish. Update: native speakers tell me that overboiling is not a real word in English. But I would have liked it to be :)

"Simmer for hours on low flame" is the term I would use for making things like katak, which are essentially an evaporation process, or just a generic term when you don't have a better description. Your goulash example will be probably called "cook until the onion disintegrates". The word "reduction" which somebody used in a comment at ELL is also restricted to evaporation-only techniques, where you start with liquids and let them sit until they lose some predetermined amount of their water (but normally does not also include curdling and/or fermenting the way katak making would). But reduction is a special case, because if it is not clear from the context that it means just evaporation, it is mostly used for the combination of deglazing and subsequent reduction, which involves pouring an acidic liquid (wine, vinegar or fruit juice) into the hot fat left after preparing meat in the pan, and then letting most of it evaporate (which happens in under a minute).

So, unless you have a very specific word for the technique you are using, you have to stay descriptive. There is no single word which encompasses all kinds of long boiling.

I don't think there is any specific phrase for that phenomenon... technique is probably too strong a word. The closest I can think of is "to cook down", as in:

I cooked the onion down until it vanished in the sauce.

Still, simply cooking or simmering or boiling would work just as well.

Take the case of split pea soup, where the entire idea is to cook the peas down until they vanish into the porridge. Most recipe simply say to simmer or cook.