Hi, I have a question related to a scenario:

I am a DM for an Icewind Dale: Rime of the Frostmaiden game and my players found the Shield Guardian Amulet and the shield guardian to match.
We then had a little combat encounter to do with the secrets and it resulted in the players shield guardian being dropped to 0hp.

In this instance, what happens to the shield guardian? Is it now dead and destroyed? Is the magic gone?

I kinda just treated it like any old monster but under the players control and given it wasn't exactly a living organism I didn't give it death saves, so to me when it dropped to 0 HP, it "died". Has anyone run it any differently or was it meant to be run differently

The shield guardian  keep going for some time. While this particular shield guardian amulet is a rare magic item that requires attunement to activate and control the shield guardian, it otherwise functions as described in the shield guardian's entry in Monster Manual, meaning it may act normally. As a matter of fact it already did once before.

This shield guardian survived the fall of Ythryn, although its master did not. After the wizard's tower crashed, the guardian left the spire to go find help but got buried in an avalanche. It eventually shut down.

Quote from ItsScottish_ >>

In this instance, what happens to the shield guardian? Is it now dead and destroyed? Is the magic gone?

It's dead unless you rule otherwise, which will render the amulet not very useful. Relevant rules:

2014

Most DMs have a monster die the instant it drops to 0 hit points, rather than having it fall unconscious and make death saving throws.

Mighty villains and special nonplayer characters are common exceptions; the DM might have them fall unconscious and follow the same rules as player characters.

2024

Monster Death. A monster dies the instant it drops to 0 Hit Points, although a Dungeon Master can ignore this rule for an individual monster and treat it like a character.

Note, however, that revivify can be cast on a construct.

Quote from Plaguescarred >>

The shield guardian  keep going for some time. While this particular shield guardian amulet is a rare magic item that requires attunement to activate and control the shield guardian, it otherwise functions as described in the shield guardian's entry in Monster Manual, meaning it may act normally. As a matter of fact it already did once before.

This shield guardian survived the fall of Ythryn, although its master did not. After the wizard's tower crashed, the guardian left the spire to go find help but got buried in an avalanche. It eventually shut down.

 

 

 Im struggling to see what point you're tryna make here apologies.

Sorry for the confusion i thought i read the player dropped to 0 hp but if it's the shield guardian then yes it's dead unless ruled otherwise.

Quote from ItsScottish_ >>

In this instance, what happens to the shield guardian? Is it now dead and destroyed? Is the magic gone?

I kinda just treated it like any old monster but under the players control and given it wasn't exactly a living organism I didn't give it death saves, so to me when it dropped to 0 HP, it "died". Has anyone run it any differently or was it meant to be run differently

You as a DM are free to do as you like. As @Pantagruel666 posted the common advice from the rules is to have monsters die at 0hp but to make exceptions for story reasons for any NPC/monster you like. IMO this would certainly qualify for that (unless you think it might unbalance the adventure, IIRC it doesn't). 

Also one thing to note, Icewind Dale is based on the 2014 rules and those are much harsher on being able to heal constructs, the 2024 rules allow most (if not all) spells that heals to also work on constructs so it wouldn't be unreasonable to allow for 2014 spells to do so in a pinch if it helps your story along.