Yes already frozen mussels are usually dead but they are safe to eat because the mussel has remained frozen and the freezing temperatures keeps the bacteria from growing.
If you just refrigerate the mussel then bacteria can grow on the dead mussels meat and then in that case the dead mussel should not be eaten.
But when mussels are commercially frozen they are usually frozen while they are fresh so if they do die then they are still safe to eat.
Also floating mussels are dead.
When the mussels float they are either dead or empty and if the mussels float they are bad and should be thrown out.
The mussels should not float and if the mussels do float it's an indicator that they are bad and dead and should not be eaten.
Eating already dead mussels even when cooked can make you sick because they can contain bacteria.
Partly opened mussels can also be dead and to test whether the mussel is dead or not squeeze the mussel shut and if it stays closed then it's good and if it does not stay shut then it's bad and should be thrown out.