The encased thing would be from a bezel. Sometimes for jewelry, ornament or keep sakes. You can still buy empty bezels made for different sized coins if you made a search. eBay also has a lot of still encased cents one can purchase.
Coppercoins.com - MadDieClashes.com - Error-ref.com
TrailDies.com - ErrorVariety.com - Port.Cuvelier.org
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