Avenging the Villain/Playing With

Basic Trope: Once the villain is defeated, their friend or relative shows up to continue fighting the hero.
 * Straight: The villain dies, and his little brother shows up shortly afterward, hating the hero for killing his sibling and out for revenge.
 * Exaggerated:
 * The villain dies, relative takes his place. And then the relative dies, but he has a friend who takes over for him, and then in his death we get his daughter who comes in... On and on.
 * Alternatively, the entire villain's family fights the hero after the villain dies.
 * Justified:
 * The villain is Affably Evil, so it's only natural that he'd have some kind of family who sympathized with him and was angered by his murder at the hands of the hero.
 * Or Alternatively the defeated villain was revealed to be framed in which someone wants to defeat the "heroes" whom were actually Unwitting Pawns of a villainous 3rd party.
 * Inverted: You Killed My Father
 * Subverted:
 * The villain dies, his daughter shows up, walks up to the hero... and thanks him for killing the villain, whom she thought was a terrible person.
 * Alternatively, the villain dies, and his brother shows up, thirsty for the hero's blood. The hero starts with the usual speech that "revenge won't bring your brother back", but the brother laughs it off. Turns out he's not trying to avenge the villain, he's just pissed that the hero was the one who killed the villain and not him.
 * Double Subverted:
 * After the villain's death, a relative of his shows up but appears to show no desire for revenge. Then another relative appears, and he's not of the same opinion there.
 * Alternatively the relative/friend/loved one of the Villain seems to be OK with this but it is then revealed that it was all an act and was plotting revenge but was only being nice about it at first just to try to get the heroes into a false sense of security.
 * Parodied: The villain's son shows up, thirsty for revenge... and six years old. He attempts to fight the heroes, who fail to take him seriously, much to their regret.
 * Deconstructed: The dead villain's friend shows up and reveals that the villain was truthfully not as bad as he looked- instead of the Complete Monster the heroes thought they were killing, he was more of a Well-Intentioned Extremist, with friends and family.
 * Reconstructed: The villain may not have been so bad, or was at least truly loved by his avenger, but vengeance eventually corrupts the new antagonist into a true Complete Monster.
 * Zig Zagged: The villain is dead, and his daughter shows up, but she wants to join the heroes. Great! Except it was an act to get closer to the heroes and then them. After a fight, the heroes show her evidence that the villain was a Complete Monster, and she seems to back down... but it was just to get the heroes' guards down. After a while, she realizes that revenge won't bring her father back, and decides to do something constructive with her life. And then the ghost of the villain possesses her and tries to kill the heroes.
 * Played For Laughs: The villain was the head of a large, branching family, and in an inspired moment of Genre Savvy, he left a will stating that "My fortune will go to the relative that avenges me." This entire branching family starts to gang up on the heroes, before The Smart Guy points out that there can be only one successor, and an Enemy Civil War breaks out. The last remaining member is too wounded to do anything, and simply limps away.
 * Played For Drama:
 * The avenger succeeds in his goal.
 * Or worse, the Avenger decides to take Revenge By Proxy, and succeeds.
 * Averted: The villain is dead. Nobody comes in to avenge him.
 * Enforced: "We can't just end the series now -- we could still milk more money out of this! Let's have someone who knew the villain come in to take his place."
 * Lampshaded: "He had friends? Uh-oh, now they're mad at us."
 * Invoked: The villain knows he'll probably be defeated soon, and sets out to make himself some friends to take over his fighting the hero if the situation comes.
 * Defied:
 * The villain dies, so the heroes make sure to kill any of his friends and family, to make sure they won't take over his position any time soon.
 * Alternatively, the heroes make sure to take the villain alive so that his friend and family won't see them as murderers.
 * Discussed: "It's like some kind of book -- kill one, another one pops up to take his place, repeat."
 * Conversed: "Oh, come on! Just end the series -- it won't be the same with the villain's mother as Big Bad -- talk about milking the cash cow."

It can't be! Emperor Evulz is dead! Never fear, I will avenge you, Evulz!