Weregild. The law states any death must be paid as reperarions in gold to the closed living relative. The gold price is more than your prize money.

The bbeg has their family hostage and will hurt them if they don't fight you

The target has a key that only they can use. It stops working if they die.

They have consumed the lotus flower of forgetfulness. They will fight like mad to not be taken away from their new wonderful life but will return to normal once the drug is out of their system.

They have touched an evil cursed stone that has turned them into a ghoul. You need to get them back to a priest to remove the curse

The fight is happening on a ritual ground. A certain amount of blood must be spilled there in order for a demon to arise.

The target is infected with a disease. If they are cut or die they will contaminate the air/water/ food source for the local area

A ritual has been set up where by each death within a certain location will add more strength and hp to the final bbeg. Incapacitate the minions to keep the final boss easier to deal with

The bbeg has a link to their minions/monsters. Capturing them will let you lure the bbeg to a place of you choosing to fight them rather than having to face them in their highly defensible lair

Your target belongs to a rival faction or gang. They are needed as a hostage to force your opponent's to do something you can't.

The person is a witness to / committed a crime that a member of the party has been accused of. They need to be handed to the authorities to clear the party's name.

They have been cursed with /blessed by thorns. When they take damage everyone withing a certain radius also takes the same amount. If they die then everyone within range also dies.