"swan song" was poor writing here, a mangled figure of speech at best. Maybe they should have sung a requiem or farewell song instead.

but what is a swan song but a requiem or farewell song?

the term comes from the believe (we now know it was a false one, but) the Mute Swans (one species of swans) only sang at the moment of their death (i suppose hunters heard them!)

there are trumpeter swans, and mute swans.. (and no doubt many varieties of swans--can't think of any, but i have seen photo's of them in the zoo) i don't think any of them have a special sound they make as they lay dying, but none the less, a swan song is still something i associate with death or at the very least a farewell.