Can you delete Facebook and keep Messenger?

It is not entirely possible for you to completely delete your Facebook and use Messenger.  But you can use Messenger event after deleting your Facebook.  This means that your account will not be reactive, but you can stay connected with your friends.

Log in to your Facebook account

 - Then go to Settings and Privacy and click on Settings.

 - Then select Your Facebook Information and then select the Deactivation and Delete option.

- Then select Deactivate Account and select the Delete Account option.

 - Then select the reason why you are leaving Facebook and click Continue.

 - Then de-select the Opt out of Receiving Messages on Messenger option from inside the pop up and then select the Deactivate option.

How to use Messenger after deactivating your Facebook account?

 - Download the Messenger app on your smartphone.

 - Then use the same email ID and password that are used inside the Facebook account and login inside Messenger.

 Then your Facebook friends can contact you from Facebook's chat window or on Messenger.