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Being drunk my person told me he lost all the money I brought him (a lot), when he was drunk, but he can't talk about it, and he'll "cover up for his error".

I felt intense compassion towards him, as he really seemed hurt, so I started to evaluate how I can mend the situation (without crossing the line where I'd start rescuing him)

Next day I requested the details and he said he faked because he wanted to "piss me off".

Okay, fine, the money is found, but I feel very unhappy. It feels like he cheated me in my best intentions. I realise it's no fault of his (he was drunk, and he is generally a troubled guy), but why he would do it - and why do I feel so cheated? After all, everything is okay, money is not lost... .but I feel physically very stressed out.

I think you may have answered your own question.  He is a troubled guy.  He will do things that don't make sense to you.  He is looking for your reaction. 

I'm currently working through the Feeling Good Handbook by Dr. David Burns.  It's helping me understand why I've been carrying negative feelings around like an albatross.  It may help to take a look at why you are feeling as you are about a situation over which you have no control.   

Agreeing with Rockylove here, he probably doesn't even understand why he does what he does.

It's possible he does not even understand how weird, inconsiderate and abnormal his behaviour seems to a 'non'? It might make sense in his head. It might also be a complete mystery to him, too.

Yeah... .never mind... .I got over it in a couple of hours... .

Maybe he wanted to make sure that I would not "reprimand" him. Or to make sure that I would. Kinda unconditional love test