Hi @[deleted] and welcome to the Community!
If you did not define any automation rule to automatically close linked tickets, then nothing will happen to your cloned ticket. Cloning is nothing more than creating a new ticket with the same information on it that was in the original ticket. Jira does indeed add a cloned link between the two issues, but this has no other purpose or effect than letting you know where the ticket was originally copied from.
From the linked issues section of either issue, you can just delete the link. It will just remove that link, without any other impact on both issues. They will continue to exist as separate issues.
Hope this helps!
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