[mothered]

when I tell them that the earbuds are missing from the package what kind of reply should I be expecting?

Impossible to say for sure.

and should I be avoiding any open cases or investigations?

No, do not avoid complying with their Investigation.

It's nothing more than company protocol to move forward with your claim.

also shipped package weighs 2.9 lbs and the package of the item itself is 2.59 lbs

You're claiming an Item was missing that's extremely light and will not be detected, so the gross/shipping weight Is Irrelevant.