Is there a way to Audit for Deletes in the application? Custom object instances were deleted from the system and you are looking for a way to Audit those Deletes.
Clarity 16.x
You can set audit trail on the Delete operation for that custom object in Studio.
You need to audit ID and/or Name attributes and when someone deletes an instance you will be able to see in the Global Audit trail under Administration menu in Classic or under Administration->Audit in Modern UX..