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Under normal circumstances, you can't earn cards for demos or free-to-play games you haven't paid for, to prevent abuse. But how does this work with the new family sharing feature?
If my brother plays one of my games under his account, do I get the cards, or does he? Do the cards get counted towards my card-allotment, or his? Or are cards simply only handed out when the owner plays?
All the cards, badges, emoticons and backgrounds can be viewed on the Steam Card Exchange website. Just find your game by its first letter.
You are probably applying one of the many games list filters (ie: installed games) - choose the game library you wish to view from this menu at the top of the steam window (the same way you would filter to show only installed games) and this will present you the available games from that library:
(On a train at the moment so higher quality screenshot will be added later)
Best Answer
Neither. From a buyers point of view, it's not fair if someone else gets the card you paid for. From a borrowers point of view, it's not really fair that someone else gets the cards with your playtime.
You said it yourself: you cannot get cards for games you haven't paid for. This holds also for games with the family sharing feature. If your brother plays a foreign-library game, which he hasn't bought yet, he will get no card drops for this game. There are even bug reports on this matter, since those game will show up in your badge process, with 0 card drops, but you're not eligible for a booster pack.
All in all, only those who paid for the game will get cards when they play the game.