I have heard in a video that I may keep the monthly games you get at Xbox Live Gold when I finish the membership is that correct
because it does not work on ps4 with ps + yes
What happens to my Games with Gold games when I cancel my Xbox Live Gold or Xbox Game Pass Ultimate subscription?
If you cancel your subscription, you will not be able to access Games with Gold titles through Xbox One. If you choose to renew your subscription, you can access and play previously used Games with Gold titles.
You can retain Games with Gold titles that you have used as an Xbox Live Gold or Xbox Game Pass Ultimate member through Xbox 360, regardless of whether you renew your subscription.
It is exactly like that.