Yes happens all the time, but you can still play it (as long as it's not online only etc.)
And if you do, does the unity pricing change now cause an install cost?
Yes, but it will still stay in your library so you can download/reinstall it.
Wow! So with this new unity pricing, even if you delete the game the developer can get charged
As much as I don't like the new Unity policy I think this is actually covered by the "No, in this case the developer is not distributing it so we’re not going to invoice the developer" FAQ answer given in response to a question about what happens if your game is install distributed through a subscription service like Xbox Game Pass. For a developer it might be worth getting that exact question answered in writing though.
It happened to Rocket League
You can still play the Steam version of Rocket League though. I know someone who still actively plays it.
I do too, the weird thing I just realized is I get updates still too
I guess they can delete the steam store page, so you can't redownload it I guess? I assume it wouldn't remove anything already on your computer.