In some unusual cases, noncreature permanents may explore. For example, if the creature card returned by Defossilize is somehow not a creature once it's on the battlefield, it can still explore. You'll take all the same actions, and you may end up putting a +1/+1 counter on the permanent. (Note that some effects target a creature, and those effects would still require a legal target to have it explore.)
Queen's Agent
If a resolving spell or ability instructs a specific creature to explore but that creature has left the battlefield, the creature still explores. If you reveal a nonland card this way, you won't put a +1/+1 counter on anything, but you may put the revealed card into your graveyard. Effects that trigger "whenever a creature you control explores" trigger if appropriate.
Some spells or abilities might cause a creature to explore multiple times in a row. If you reveal a nonland card when a creature explores and leave it on top of your library, then the creature explores again immediately afterwards, you'll reveal the same card again.
Magic: The Gathering · ™ & © Wizards of the Coast · Illus. Winona Nelson
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