Does anyone know if you are sharing Apple ID if you will also receive any incoming calls and can deny them?

If they are sharing an ID, they will receive incoming calls and could deny the call. My suggestion is they need to stop their relationship with that person and prevent them from sharing the Apple ID.

As a precaution, change the password.

 Apple ID Password Change.   -   

 What to do after you change your Apple ID or password - Apple Support  -   I suggest doing this before you change your Apple ID or password.

Link to contact Apple Support in the article.

Apple ID has been compromised.      *

Security and your Apple ID.   *

Device and Data Access when Personal Safety is At Risk    -

Checklist: If you want to see if anyone else has access to your device or accounts  *

They can also change the Apple ID email address. Note the restrictions in the article.

Apple ID Name Change.  * 

 What to do after you change your Apple ID or password - Apple Support  *  I suggest doing this before you change your Apple ID or password.

When you share an AppleID, you share totally equal access to everything associated with that AppleID. It’s no different than any other online services login ID. If you share a bank account login ID, you share equal access to the bank account. If you share a GrubHub login ID, you share equal access to that GrubHub account (including payment information). Same goes for any other online service and its login ID.

The systems using the login ID has no way of knowing the individual human being who is using it. They only know the login ID accessing data and information. Since it’s the same login ID, the system grants equal access to anyone (and everyone) using that login ID.

There is absolutely no privacy nor separation of data and access when you share any online services login ID, and an AppleID is no different since it is nothing more than an Apple services login ID.