Is it possible to make  a game unlisted—not coming up in searches or category browsing—AND/OR... if someone does have the link to it, they can't download it UNLESS they already bought it?

I don't want to shut down the game for existing users—I want them to easily get to the game from their Library the same as always. I want them to be able to re-download at will, and I intend to even offer them future updates... But I'm considering stopping NEW users from getting it.

(Setting an absurdly high price to discourage new purchases is not very user friendly—so I won't do that.)

Thanks in advance!