If Cartouche of Strength leaves the battlefield before its triggered ability resolves, the creature it last enchanted will fight the target creature if it's still on the battlefield at that time. However, it won't have +1/+1 from Cartouche of Strength anymore.

Each Cartouche is an Aura with "Enchant creature you control." If another player gains control of either the Cartouche or the enchanted creature (but not both), then the Cartouche will be enchanting an illegal permanent and be put into its owner's graveyard as a state-based action.

The enchanted creature has +1/+1 and trample while it's fighting. However, trample doesn't apply during a fight.

If the triggered ability's target is illegal when it tries to resolve, or if the enchanted creature has left the battlefield, no creature will deal or be dealt damage.

Cartouche is an enchantment subtype with no special meaning. Other cards may care about which enchantments are Cartouches.

If the target creature becomes an illegal target before a Cartouche spell resolves, the spell doesn't resolve. It doesn't enter the battlefield.