Is the name written in the book page? Or on the cover-

@ExistenceNull  
Only the person that came up with this idea of ‘Hag Warder’ could tell you exactly, but one could consider a creature, as such, to be ‘dead and gone’ when whatever they have to ‘run them’ is destroyed. The instance you speak of is ‘destroying what makes them ‘alive’’ while leaving behind a shell. IF this is an instance where whatever ‘soul’ the creature has inside of it remains.(Instead of being sent to ‘Mu’ in Death Note) then one could, theoretically, revive them, yes. Since we are going by Death Note rules than the thing killed by the Note will be ‘sent to Mu.’. Not sure if the Death Note was ever SUPPOSE to be used on anything, but humans. I mean… it never states it during the series, but do animals have souls? It would help to clear things up if that was known.
 
The simple fact is that this was a humorous mistake on this creatures part that they will have a few minutes to regret if their face is anything to go by. :3

@Xaxu-Slyph  
I beleive there was a rule that stated an upper limit for the time you were allowed to specify.  
But Wetweave here is a Hag Warder, a form of sapient construct that hunts nightmare creatures.  
But as for their anatomy, from what I’ve seen it’s less complex then an organic but there are some fascimilies, most of which aren’t actually necessary for their function.  
It might be possible that their design contains an enchantment or otherwise designed magical algorithm/program that has enough similarities to be counted as a heart, but would it actually terminate them or be the equivelant of destroying a power supply but leaving the hard drive intact?

@ExistenceNull  
I’m not sure what ‘Warders’ are as I was only reacting to the image.(Unbeknownst to me about this ‘species’?), but the Death Note’s ‘rule’ about ‘Those whose names are written in the Note without a cause of death will die of a heart attack in ‘x’ amount of minutes’ was there as a way to kill them simply without a specific reason. I suppose to give them time to write in something if they changed their mind. Now… if we want to get technical. Mayhaps the Death Note refers to the ‘heart’ of a creature being ‘what makes it run’. In this instance… if this creature has a consciousness and a ‘life force’ then, mayhaps, the Death Note takes this into consideration and destroys whatever makes this thing ‘tick’. That’s just a theory in this case as the Death Note series takes place in a predominately human world. Meaning that anything that dies will most likely be human.(Do they ever use it to kill animals? Not sure if that even works…
 
A further inquiry(And realize it HAS been a long time since I read the series…) If one puts in like… oh… ‘Light Yagami dies at the age of 106 in good health and mind’. Does that happen or was there a rule that dictated that they cannot die ‘beyond their original life count’? Not sure, but it’s something to think about if the rules didn’t dictate that. :3

@Xaxu-Slyph  
Question, do the Warders have hearts?  
Because how could the deathnote kill something that is by technicallity a construct of artificial material?

“…What Have I DONE!?”

Now yah mucked up.