There are two types of
CIC BJ chips, V6 and V7, and their construction differs. With the V7 chips, the plastic is molded around two coins that are back-to-back (without glue). They end up sitting in a groove inside the plastic, so the only way to get them out would be to break that plastic frame. Example of a V7 shown for reference below.
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On the V6 line the plastic is molded first, then coins applied on each side with glue in the middle. The plastic has a slight, thin lip on the inside to create a recess for the coins to sit in, so they don't simply fall through the center and it leaves room for the glue as well. As
@kaimat mentioned, sometimes the coins may pop out due to old age or perhaps very little glue actually used. I think it might be possible to remove V6 coins if you can affect the glue's adhesive ability, perhaps by putting the chips in the freezer for a while (I have not tried). But the inside lip is thin and seems quite delicate, if it gets destroyed in the process you won't really be able to replace the coins with anything.
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