RSBM
@Emma Peel
Please understand that I am tiptoeing when answering this question.
The rules of evidence are very generalized rules, not hard and fast and are not created to address specific issues. Federal Rule of Evidence 401 and 402 lay out the main intent of the rules of evidence.
401: Defines relevant
Evidence is relevant if
(a) it has any tendency to make a fact more or less probable than it would be without the evidence; and
(b) the fact is of consequence in determining the action.
402: basically just says relevant evidence is admissible; irrelevant evidence is not.
All other rules that flow from these two maxims deal with reliability of evidence.
So the default position is to include all relevant evidence. In the case of an item which lacks chain of custody, this obviously brings up a question of reliability. Rule 901 speaks to these types of issues, and says, in general: to satisfy the requirement of authenticating or identifying an item of evidence, the proponent must produce evidence sufficient to support a finding that the item is what the proponent claims it is. Rule 104 also instructive, but I won't delve too deeply into it.
A court (judge) might deal with this issue by excluding, or by allowing but giving a limiting instruction to the jury as to the lack of reliability of the evidence (basically meaning the judge would instruct the jury to give this evidence less importance to that particular item). It could also require it to be authenticated by introducing witness testimony as to the chain of custody.
It is a lot to read, but I think you would find the comments of the rules I listed as helpful (Rules 104, 401, 402, and 901):
www.law.cornell.edu