Case of the Burning Masks

If multiple creatures you control deal combat damage, each one counts as a source that dealt damage that turn. A single creature that deals combat damage multiple times in a turn (due to double strike or additional combats) still counts as only one source.

Cases don't lose their other abilities when they become solved.

"Solved — [Triggered ability]" means "[Triggered ability]. This ability triggers only if this Case is solved." Triggered abilities use the word "when," "whenever," or "at." They're often written as "[Trigger condition], [effect]."

Something that changes zones becomes a new object in that zone and will therefore be a new source. For example, if you cast Flametongue Kavu, deal damage with its enters-the-battlefield ability, exile and return it to the battlefield with Momentary Blink, deal damage again, then cast Momentary Blink with flashback on Flametongue Kavu to repeat the process one more time, you've fulfilled Case of the Burning Masks's "to solve" trigger condition. 

"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."

You need to control the sources that dealt damage only at the times when they dealt damage. If they die or change control after that point, the "to solve" ability will still trigger at the beginning of your end step as long as you still control Case of the Burning Masks.