.

got three great answers, up here, and yours adds a useful plus. thank you all!

my guess? it's forever, 'cause you've got the key!

oh my

Well, I still have Rusty Hearts (a long dead and removed from the store MMO) in my Library and even the option to "Install" it. It's marked as "Complimentary" in the Licenses list with the usual single button removal option. As with other removed games its Steam Community Hub is still there.

So for merely removed games the answer is definitely that you get to keep it.
I'm not sure if it's the same for games where Steam directly terminated the contract though (aka, for scam games). I don't have any of those (and haven't committed any to memory) to check if they still have Steam IDs or if they get completely wiped.

Valve changed the handling of free licenses a while ago.
Before when you only hit Install, it was temporary until deinstallation. To keep it permanently, you had to either keep it installed or activate by key (a DLC sufficed). People called the latter binding.
Now if you add a free license, you don't have to install anymore to keep it permanently. Game being removed or banned doesn't harm at all.

Playing depends on files still working, if online game: server still running, but an offline game should still work afterwards.
And as others have mentioned before, there are the differences regarding profile features (if the game wasn't profile features limited anyway). So you will still see collectors looking for keys for F2P games.

I mean, yeah... but since dropping booster packs requires being able to drop cards in the first place, I feel like this was already obvious.