Probably not, but there is an argument worth considering when you make a ruling
First, I present an argument in favor of “No, it cannot use its reaction”. Then, I present a counter argument that one should at least consider when making a ruling.
Under the sleep spell, it cannot be used.
Sleep the spell imposes the unconscious condition:
- An unconscious creature is incapacitated, can’t move or speak, and is unaware of its surroundings.
The incapacitated condition states:
An incapacitated creature can’t take actions or reactions.
Since Unstoppable requires use of your reaction, it is unavailable while asleep via the sleep spell, as you are asleep at the time the reaction trigger occurs.
Regular sleep is under-defined unless you use Xanathar’s Guide.
The rules for sleeping given in the Player’s Handbook do not tell us that regular sleeping imposes any conditions, so it will be up to the DM to decide if sleeping imposes any condition which restricts use of your reaction. However, if you are using Xanathar’s Guide, which is optional (ask your DM), we have more clearly defined rules:
Just as in the real world, D&D characters spend many hours sleeping, most often as part of a long rest. Most monsters also need to sleep. While a creature sleeps, it is subjected to the unconscious condition. Here are a few rules that expand on that basic fact.
If using this rule, Death’s Head of Bhaal cannot use its reaction while sleeping (see first section), even conventional sleep not imposed by a spell.
This is how I have ruled before about characters using reactions in their sleep, and I think this is far more intuitive than the argument I present below.
Next, I present a case that it can use its reaction to negate the damage that wakes it up.
The reaction occurs after the trigger.
The rules for Adjudicating Reaction Timing state:
Various spells and features give a creature more reaction options, and sometimes the timing of a reaction can be difficult to adjudicate. Use this rule of thumb: follow whatever timing is specified in the reaction’s description. For example, the opportunity attack and the shield spell are clear about the fact that they can interrupt their triggers. If a reaction has no timing specified, or the timing is unclear, the reaction occurs after its trigger finishes, as in the Ready action.
No timing for Unstoppable is described, so the reaction definitively happens after taking damage. But if it happens after taking damage, the sleep spell states:
each creature affected by this spell falls unconscious until the spell ends, the sleeper takes damage
So the sleeper also wakes up after taking damage. So “wake up” and “Unstoppable” would be simultaneous effects, and an optional rule from Xanathar’s Guide tells us how to rule on simultaneous effects:
Most effects in the game happen in succession, following an order set by the rules or the DM. In rare cases, effects can happen at the same time, especially at the start or end of a creature’s turn. If two or more things happen at the same time on a character or monster’s turn, the person at the game table — whether player or DM — who controls that creature decides the order in which those things happen.
Since they are both responses the taking damage they happen at the same time, and the player controlling Death’s Head can choose which order they happen in.
To be clear, I would not rule this way, and I think it is rather unintuitive compared to ruling the other way, but the ruling is not entirely unsupported; it just gets way into the weeds of patching together a ruling from under-defined rules.
tl;dr Reaction timing is often quite ambiguous, but here, you probably can’t use your reaction while you’re asleep, even if the trigger wakes you up.