In two senses:
1. an active comet boils off all its volatiles and no longer grows a tail near the Sun, it becomes a dead lump. If it's 'dead' now, it must have been 'alive' then.
2. anything carved into rock still attached to it's parent bedrock (as opposed to quarried from the parent rock) is said to be carved from 'living rock'.
Funny language, English...
A nice summation :)