Failed Background Check: Dismissed due bad performance

I was let go from my old firm as an analyst. I have now secured an offer but was informed from a friend at that place, that the firm calls people from your former employers to check upon you.

Now, when I applied to the new firm I was still employed at my old firm and let off during the interview process. I did lot volunteer and tell the firm I was interviewing that I have been let go.

Now I am scared that the new firm will call my former firm and inquire about me. I did get a reference upon leaving the firm which wasn’t too bad. However, I am afraid of the informal chats e.g. one associate calls another one or a Partner calls a MD.

Thanks