Indeed it is a BIE. The chip does not need to connect to be called a BIE. In fact most such chips, even if they are between other letters such as the IB or RT are known as BIEs since they are a class of die errors caused by die chips between the letters of LIBERTY.
Furthermore, this chip does actually extend all the way between the letters B and E, so would be a "full" BIE. If it had not extended between them, it would be an "associated" BIE. This is terminology from Jean Cohen. The
Cuds on Coins terminology may be a bit different, as the COC scheme is generally based on Hardy.
1957-D was a banner year for BIEs. A quick look shows that this might be one of these:
B402: does the coin have an RPM?
B346: does the coin have a crack lower right wheat to rim?
B323
I have not cross-referenced to see if COC has examples of the above, but that might be useful for you to do.
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