If you were magically linked with someone to be immortal and one person had lived long enough that they wanted to die, how would you deal with it?

The rules are that neither of you can be killed except by each other, but if one of you kills the other, you both die.

You are happy to continue to live, you're happy with immortality but your partner is sick of it and wants the eternal torture to end and so is dead set on killing you.

How do you deal with their constant attacks?