Being solved is not part of a permanent's copiable values. A permanent that becomes a copy of a solved Case is not solved. A solved Case that somehow becomes a copy of a different Case stays solved.
Case of the Crimson Pulse
"To solve" abilities will check for their condition twice: once when the ability would trigger, and once when it resolves. If the condition isn't true at the beginning of your end step, the ability won't trigger at all. If the condition isn't true when the ability resolves, the Case won't become solved.
"Solved — [static ability]" means "As long as this Case is solved, [static ability]." Static abilities are written as statements, such as "Creatures you control get +1/+1" or "Instant and sorcery spells you cast cost {1} less to cast."
Magic: The Gathering · ™ & © Wizards of the Coast · Illus. Adam Paquette
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