Kokua Line: How do we avoid fire risk of stored lithium-ion batteries?

Lithium-ion battery backup devices present fire risks, leading to airline bans in checked luggage. Users are seeking guidance on safe home storage for these devices when not in use. Recent incidents of batteries bursting into flames have prompted safety warnings.
Question: Recently there have been warnings (and at least one incident) that phone battery backup devices can burst into flames. Airlines forbid them in checked luggage. So, assuming there is a legitimate concern, what should we do at home? I have one, fully charged in a drawer. Is that a problem? How should we store them when not using them?
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