My PCs have just brought Strahd to 0 hp, and as per the rules Strahd has turned in to a mist cloud, and next session will start heading to his coffin.

The description of Strahd's mist form specifically calls out the fact that in mist form he has advantage on certain saving throws, and can only be damaged by magical weapons. This seems to imply that in mist form he can be attacked.

If he is in mist form by choice, and still has HP remaining, then it makes sense. If PCs attack him in mist form while he has HP, successful attacks subtract from his HP.

But what if he is forced into mist form by being reduced to 0 HP? If he is attacked in this state, he has no HP from which to deduct. Does each successful hit count as one failed Death Save for Strahd, and after three such failed saves he is completely destroyed?

How have other DMs dealt with this?

Short answer ... your call. It’s Strahd though,  he is ancient, he is the land ...

Mist form pretty useless if you can just whack at it with +1 longsword or magic missile it and kill him for good. If there is other mist around would count it at least as invisible condition. He would vanish immediately into the mists. He can enter another creatures space ... his about another creature 💀 entirely 🤔!!

If fight was epic and your group did a great job - go for it ! 

In the Epilogue, under Strahd Dies is the following:

The vampire must be in his resting place to be utterly destroyed.

I didn't see anything under Misty Escape indicating advantage on saving throws and impervious to non-magical damage.  Where did you see that?

Personally, I would run it with the Mist form being impervious to damage, forcing a final confrontation at the coffin.

Edit: sorry, I ignored the Shapechanger ability.  I stand by my opinion, though, and would just treat the Misty Escape form as different from the Shapechanger (Mist) form in this respect.

Specific beats general - so while a creature in mist form is generally still capable of taking damage and would be killed/destroyed if that damage triggered the normal death rules (either by dealing the creatures maximum hp in damage with one attack, or by totaling up 3 failed death saves), Strahd specifically can only actually be destroyed if he is in his resting place.

As my party is getting close to that point, I interpreted it as a way they could steer the mist if they were trying to for e him into the coffin to be destroyed. No damage to Strahd, but stuff that he’d want to avoid. 

In the end I had swarms of bats fly up out of the crypts to cover his escape so they never even got close to him in mist form. He made it through the wall in the staircase from the chapel down, and the PCs had to race through the castle to get there. When they did get there, I had Vladimir Horngaard show up to try to stop them from "giving Strahd peace". A PC and Esmerelda were dropped by Vladimir before the barbarian pushed him into the teleport trap. Then the rogue and barbarian teleported into Strahd's crypt.

I had the rogue make Strength checks to pound the steak into Strahd while the barbarian had to fight off the three vampire brides. It got really tense when the rogue rolled a 3 on one of his strength checks. I had Strahd open his eyes and grab the rogue by the throat, but on his next action the rogue rolled a good Strength check and drove the stake home, destroying Strahd and causing the castle to begin collapsing.

Nice!  That sounds like a truly epic conclusion.  Congrats!

It's all up to how you want to do it.

What we did:

My group that was a very optimized holy party and got all the fortune treasures made quick work of Stradh in one vs the group combat (I only had bad rolls). They had already been in the catacombs exploring the castle and cleansed a lot of the monsters that lurked there.

When Stradh turned into mist he just entered a wall and floated down to his coffin and there was a sprinting gauntlet to rush down and finally kill him to get out of Barovia. They where successful and the mad mage teleported them back to Waterdeep.

In my campaign the time in Barovia is totally different then from the prime material plane, the party was in the demi-plane of dread for a very long time but when they returned to Waterdeep only two days had passed (it enhanced the horror). But they did not kill Baba Lysaga and so she did resurrect him some years later in Barovia time (anyhow I would have resurrected him in some other way, the mists will never permanently depart Ravenloft).

In the end the characters got a letter from Stradh in Waterdeep congratulating them on their effort and promised that he will not make the same mistake on the next group of adventures. He also did a subtle threat that he will always get his way in the end and their eventual offspring should always look out for the mists for a day when he claims revenge, he can wait an eternity but they can not.

For me and the players it was a good horror ending to a D&D horror story

Very cool. I did something similar with time, every day in Barovia was 2 days in Faerun, and on their return almost a month has passed since they left, and the giants have been busy (Storm King's Thunder).

I like your taunting letter from Strahd. In my game I had evil versions of the PCs show up, and they also found other evidence of past versions of themselves in Barovia, including a crypt in the catacombs. Strahd basically told them it wasn't the first time they'd been to Barovia, and wouldn't be the last!

If anyone is currently running the COS campaign, and wants to play a haunting reading of the Tome of Strahd for their players to really set the mood then please consider clicking the link bleow:

https://youtu.be/Mlt8caF081g

What happens if Strahd is dropped to 0 hitpoints with the Sunblade or while in sunlight?

When I ran CoS, all my players had a minimuum of 20 years experienc playing the game. :)

One of the first thing the Light domain cleric did upon entering the Realm of Terror was have a hand held set of bellows made which he then proceeded to waterproof with his Alchemy Supplies.

Once he had enough silver, he started making holy water with the Ceremony spell. He always had 1-2 vials of holy water in his belows.

Whenever he forced a vampire into kist form, he's try to suck the poor thing into his belows . . .

Quote from Thucydides >>

What happens if Strahd is dropped to 0 hitpoints with the Sunblade or while in sunlight?

 If the mist form is in sunlight it's destroyed. So he is destroyed in both scenarios. 

Quote from Lazorne >>

 

In my campaign the time in Barovia is totally different then from the prime material plane, the party was in the demi-plane of dread for a very long time but when they returned to Waterdeep only two days had passed (it enhanced the horror). But they did not kill Baba Lysaga and so she did resurrect him some years later in Barovia time (anyhow I would have resurrected him in some other way, the mists will never permanently depart Ravenloft).

 

 In the CoS book on page 208 under "Aftermath" it says that Strahd reforms after some months, so really Strahd can't be permanently destroyed. The letter is a very nice touch.