Makes sense: when life will end, Death will still be there.

Surely death dies with life? Once there's no life, there can be no more death.

It very much depends on how you define Death - if it's "the absence of life", then it will stick around. Still, even if you go for "the termination of life", it will out-exist Life by an instant more.

(For the record, I'm just parroting Neil Gaiman's excellent work on the Sandman saga...)