In this example:
Agamemnon comes home to be killed by his wife and her lover.
We are quite sure that he didn't plan on dying, so comes home to be killed is not the “infinitive of purpose”. What is it then? Is there a grammatical term for that?
Edited, another example:
She came home to pick her car.
Here, to pick is the “infinitive of purpose”. In contrast:
She came home to find the house has burned to the ground.
Here, though, to find is not the “infinitive of purpose”, so what kind of infinitive is it?