What are the benefits of last rites to a mortally injured person in the Catholic belief? If a person is a unbeliever and has been injured in a way that there is no hope of survival and has never accepted Jesus Christ as Savior, does the Catholic Church believe that last rites performed with this person will bring salvation to this person.  I understand that anyone can be saved upon their deathbed but suppose this person was unconscious and never regained consciousness, would last rites still be performed and belief that this would save the person's soul?

Of course this questions is geared towards the Catholic community and Church.
From the Catechism of the Council of Trent:

The Effects of Extreme Unction
The advantages we receive from this Sacrament are also to be
accurately explained, so that if nothing else can allure the faithful
to its reception, they may be induced at least by its utility; for we
are naturally disposed to measure almost all things by our interests.
Pastors, therefore, should teach that by this Sacrament is imparted
grace that remits sins, and especially lighter, or as they are
commonly called, venial sins; for mortal sins are removed by the
Sacrament of Penance. Extreme Unction was not instituted primarily for
the remission of grave offences; only Baptism and Penance accomplish
this directly.
Another advantage of the Sacred Unction is that it liberates the soul
from the languor and infirmity which it contracted from sins, and from
all the other remains of sin. The time most opportune for this cure is
when we are afflicted with severe illness and danger to life impends,
for it has been implanted in man by nature to dread no human
visitation so much as death. This dread is greatly augmented by the
recollection of our past sins, especially if our conscience accuses us
of grave offences; for it is written: They shall come with fear at the
thought of their sins, and their iniquities shall stand against them
to convict them. Another source of vehement anguish is the anxious
thought that we must soon afterwards stand before the judgment seat of
God, who will pass on us a sentence of strictest justice according to
our deserts. It often happens that, struck with this terror, the
faithful feel themselves deeply agitated; and nothing conduces more to
a tranquil death than to banish sadness, await with a joyous mind the
coming of our Lord, and be ready willingly to surrender the deposit
entrusted whenever it shall be His will to demand it back. To free the
minds of the faithful from this solicitude, and fill the soul with
pious and holy joy is, then, an effect of the Sacrament of Extreme
Unction.
From it, moreover, we derive another advantage, which may justly be
deemed the greatest of all. For although the enemy of the human race
never ceases, while we live, to meditate our ruin and destruction, yet
at no time does he more violently use every effort utterly to destroy
us, and, if possible, deprive us of all hope of the divine mercy, than
when he sees the last day of life approach. Therefore arms and
strength are supplied to the faithful in this Sacrament to enable them
to break the violence and impetuosity of the adversary, and to fight
bravely against him; for the soul of the sick is relieved and
encouraged by the hope of the divine goodness, strengthened by which
it bears more lightly ail the burdens of sickness, and eludes with
greater ease the artifice and cunning of the devil who lies in wait
for it.
Finally, the recovery of health, if indeed advantageous, is another
effect of this Sacrament. And if in our days the sick obtain this
effect less frequently, this is to be attributed, not to any defect of
the Sacrament, but rather to the weaker faith of a great part of those
who are anointed with the sacred oil, or by whom it is administered;
for the Evangelist bears witness that the Lord wrought not many
miracles among His own, because of their unbelief.
It may also be truly said at the Christian religion, since it has
struck its roots more deeply in the minds of men, stands now less in
need of the aids of such miracles than it did formerly, at the
commencement of the rising Church. Nevertheless, faith should be
strongly excited in this respect, and whatever it may please God in
His wisdom to do with regard to the health of the body, the faithful
ought to rely on a sure hope of attaining, by virtue of this sacred
oil, health of the soul, and of experiencing, should the hour of their
departure from life be at hand, the fruit of that glorious assurance:
Blessed are the dead who die in the Lord.