Equipment is dropped by units whenever they die, even if this death is through their duration running out. The equipment would not have disappeared with Alazkan's mirror image
Hidden wears of from combat or casting, but the actual invisible promotion never does.
The equipment is destroyed because of his HN status; the SDK does not allow HN units to capture anything. Thus, any HN unit that "captures" any equipment will destroy it instantly. My modmod will change this, as I decided to allow HN units to capture units as easily as non HN units. Thus you can take equipment, capture slaves, and spawn werewolves and giant spiders with HN units. (I may make HN units give HN to the units thay spawn/capture too, so you won't know what civ is turning all your units to slaves or who controls those werewolves that are rampaging through your territory.) I'm not letting HN units enter rival cities though, so you cannot take territory from a rival without declaring war.
Alazkan would likely destroy equipment even if he weren't HN, albeit not as often. He starts with the Marksman promotion, which causes him to attack the weakest unit in a stack. In order to capture a unit you must move into its tile when you defeat it. Because the stronger units are still there, units with marksman cannot move into the tile, and so the weakest unit (be it equipment, a worker, a slave, whatever) is simply killed. A Marksman can capture equipment, but only if no units whit any combat strength are left to defend the tile. I'll also look into changing the marksman mechanic, so that in my modmod units with no unitcombat will cannot be targeted by the promotion. This would save workers, slaves, equipment, and great people, because it would only let you attck them when they could be captured.
(I'm letting all the great people except adventurers and great commanders be captured. The Great commander promotion will be a prereq for other promotion, so I'm removing the ability to split commanders. I am however going to treat them like uncapturable equipment so that if the commander's unit is destroyed but the rest of the stack is saved that he can be joined to a new unit. Also, I'm adding the BtS military instructor great specialist (+2 xp each to units build in the city) and letting commanders join cities as them. They will also be able to build the Code of Junil, and I may make some Order buildings provide a free military instructor specialist. I made another "Local Legend" specialist that Adventurers can become, which grants +1 xp, +2 Adventurer GPP, and +3 culture. Also, any Grigori unit with hero can cast a spell reverting it to an adventurer, so adventurers can take advantages of promotions available to any unit.)
(I joke)