Todas as indicações são de que o Mestre Sith matará o aprendiz e assumirá um novo. Dito isso, o Mestre tem poder absoluto e pode teoricamente escolher poupar a vida do aprendiz para evitar ter para começar tudo de novo com um novo aprendiz.
Canon
A melhor descrição de cânone que eu conheço sobre como a regra de duas funções é:
Soon after destroying the Jedi, the Emperor had told Vader that he would one day be tempted to kill him. He’d said that the relationship between Sith apprentice and Master was symbiotic but in a delicate balance. An apprentice owed his Master loyalty. A Master owed his apprentice knowledge and must show only strength. But the obligations were reciprocal and contingent. Should either fail in his obligation, it was the duty of the other to destroy him. The Force required it. Since before the Clone Wars, Vader’s Master had never shown anything but strength, and so Vader intended to show nothing but loyalty. In that way, their mutual rule was secure. Perhaps Vader would attempt to kill his Master one day. Sith apprentices ordinarily did. They must, if they were trained well. An apprentice was unquestioningly loyal until the moment he wasn’t. Both Master and apprentice knew this.
Lords of the Sith, p. 27
Esta citação deixa claro que era o dever do Mestre destruir o aprendiz se o aprendiz mostrasse deslealdade. A citação também deixa claro que o aprendiz deveria mostrar deslealdade no momento em que o aprendiz desafiou o Mestre. Tomados em conjunto, isso parece ser uma evidência clara de que o Mestre Sith destruiria o aprendiz se o aprendiz desafiasse o Mestre, mas fosse derrotado.
Legends
Há descrições muito melhores da Regra de Dois em Legends, e em Legends temos acesso ao pensamento de Darth Bane e seu aprendiz - os dois Lordes Sith com a melhor compreensão da Regra de Dois.
Darth Bane estava decidido a matar seu aprendiz, chamado Darth Zannah em Legends, se ela o confrontasse e falhasse, mesmo que isso o deixasse sem um aprendiz e um corpo falido:
[Bane thinking to himself] An apprentice had to earn the title of Dark Lord, wresting it from the Master in a confrontation that pushed them both to the edge of their abilities. If Zannah intended to challenge him only after he was crippled by illness and infirmity, then she was unfit to be his heir. Yet Bane was not willing to initiate their confrontation himself. If he fell, the Sith would be ruled by a Master who did not accept or understand the key principle upon which the new Order had been founded. If he was victorious, he would be left without an apprentice, and his failing body would give out long before he could find and properly train another.
Dynasty of Evil, p. 11
Darth Zannah também pensou que Darth Bane iria matá-la se ela falhasse enquanto o desafiava:
[Zannah speaking] The Master will train his apprentice in the ways of the Sith, until one day she must challenge him. If she proves unworthy, the Master will destroy her and choose a new apprentice. If she proves the stronger, the Master will fall and she will become the new Dark Lord of the Sith, and choose an apprentice of her own.”
Dynasty of Evil, p. 153
Parece claro que a Regra de Dois exigia que o Mestre matasse o aprendiz fracassado, mesmo que o Mestre estivesse com problemas de saúde, e isso vem dos dois Sith Lords que mais se familiarizaram com a Regra.