My game got removed from my library

Have you checked your purchase history? It will show the status of the purchase there.

Hello, first it's a pleasure to be able to help you today.

My name is welcome to the community.

Hello GamerDuSiecle, all game purchases or subscriptions are registered to your Microsoft account.

Click on the link below and log in with the account you use to play and made these purchases, then go to your Purchase History and click on Refund/Returned and see if can find your Forza 4 in that section.

https://account.microsoft.com

I would like to clarify, you were able to get the game through games with gold?

No other account had gold at the time except mine if I remember correctly.

It may mean that it's not the account where the game was purchased. Kindly check other Microsoft accounts that you have.