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According to the Matysa Purana, the events of the Srimad Bhagavatam took place during the Sarasvata Kalpa.

When was the Sarasvata Kalpa? Currently, we're in the Sveta Varaha Kalpa.

And who is it referring to by "degraded men"?

Saraswata Kalpa is as same as Sveta Varaha Kalpa only.

In the Mahabharata 12:350(Shanti Parva), previous birth of Vyasa is narrated. After Brahma was created from the navel of Narayana, the goddess of intelligence (Buddhi) upon the orders of Narayana entered into Brahma, then Brahma finished the creation. Thereafter Vishnu decided to incarnate in the earth whenever Adharma arises.

After this, the original Creator of the universe once more uttered the
syllable, Bho, causing the atmosphere to resound with it. From this
syllable of speech (Saraswati) arose a Rishi of the name Saraswat. The
son, thus born of the Speech of Narayana, came to be, also called by
the name of Apantara-tamas. Endued with great puissance, he was fully
conversant with the past, the present, and the future. Firm in the
observance of vows, he was truthful in speech. Unto that Rishi who, after
birth, had bowed his head unto Narayana, the latter, who was the
original Creator of all the deities and possessed of a nature that was
immutable, said those words: Thou shouldst devote thy attention to the
distribution of the Vedas, O foremost of all persons endued with
intelligence. Do thou, therefore, O ascetic, accomplish what I
command thee.In obedience to this command of the Supreme Lord from
whose Speech the Rishi Apantaratamas sprang into existence, the
latter, in the Manvantara K.M Ganguli wrongly translated this as "in the Kalpa" instead of "in the Manvantara" named after the Self-born Manu(swayambhu Manu), distributed and
arranged the Vedas. For that act of the Rishi, the illustrious Hari
became gratified with him, as also for his well-performed penances,
his vow and observances, and his restraint of the senses or passions.
Addressing him,

Narayana said, At each Manwantara, O son, thou wilt
act in this way with respect to the Vedas. Thou shalt, in consequence
of this act of thine, be immutable, O regenerate one, and incapable of
being transcended by any one. When the Kali age will set in, certain
princes of Bharata's line, to be called by the name of Kauravas, will
take their birth from thee. They will be celebrated over the Earth as
high-souled princes ruling over powerful kingdoms. Born of thee,
dissensions will break out among them ending in their destruction at
one another's hands excepting yourself. O foremost of regenerate
persons, in that age also, endued with austere penances, thou wilt
distribute the Vedas into diverse classes. Indeed, in that dark age,
thy complexion will become dark.

Thou shalt cause diverse kinds of
duties to flow and diverse kinds of knowledge also. Although endued
with austere penances, yet thou shalt never be able to free thyself
from desire and attachment to the world. Thy son, however, will be
freed from every attachment like unto the Supreme Soul, through the
grace of Madhava. It will not be otherwise. He whom learned Brahmanas
call the mind-born son of the Grandsire, viz., Vasishtha endued with
great intelligence and like unto an ocean of penances, and whose
splendour transcends that of the Sun himself, will be the progenitor
of a race in which a great Rishi of the name of Parasara, possessed of
mighty energy and prowess, will take his birth. That foremost of
persons, that ocean of Vedas, that abode of penances, will become thy
sire (when thou wilt take birth in the Kali age). Thou shalt take thy
birth as the son of a maiden residing in the house of her sire,
through an act of congress with the great Rishi Parasara. Doubts thou wilt have none with respect to the imports of things past,
present, and future. Endued with penances and instructed by me, thou
wilt behold the incidents of thousands and thousands of ages long past
away. Thou wilt see through thousands and thousands of ages also in
the future. Thou shalt, in that birth, behold me, O ascetic,--me that
am without birth and death,--incarnated on Earth (as Krishna of Yadu's
race), armed with the discus. All this will happen to thee, O ascetic,
through the merit that will be thine in consequence of thy ceaseless
devotion to me. These words of mine will never be otherwise.

Thou
shalt be one of the foremost of creatures. Great shall be thy fame.
Surya's son Sani (Saturn) will, in a future Kalpa, take birth as the
great Manu of that period. During that Manwantara, O son, thou shalt,
in respect of merits, be superior to even the Manus of the several
periods. Without doubt, thou shalt be so through my grace. Whatever
exists in the world represents the result of my exertion. The thoughts
of others may not correspond with their acts. As regards myself,
however, I always ordain what I think, without the least impediment!
Having said these words unto the Rishi Apantaratamas, otherwise called
by the name of Saraswat, the Supreme Lord dismissed him, saying unto
him. Go. I am he that was born as Apantaratamas through the command
of Hari. Once more have I taken birth as the celebrated
Krishna-Dwaipayana, a delighter of the race of Vasishtha. I have thus
told you, my dear disciples, the circumstances, of my own former birth
which was due to the grace of Narayana in so much that I was a very
portion of Narayana himself.

Summary

• The creator of the universe uttered the syllable of speech
  (Saraswati). From that syllable arosed a Rishi named Saraswat, who
  was called by the name Apantara-tamas.


• He in the Swayambhu manvantara distributed the Vedas. Because of
  this, Lord Narayana became very happy and said to him that
  Saraswat will be born in the Kali Yuga when Kauravas take birth.
  Narayana also said in that birth his complexion will be
  dark(krishna Dwaipayana).


• Narayana said he will be born in the lineage of Vasishtha to
  Parashara, (We all know that Vyasa was the son of Parashara) in
  the Manvantara when sun god vivasvan's son Shani (i.e.,
  vaivaswata) will be the Manu.

Conclusion

The current Kalpa is called Sveta Varaha Kalpa because Varaha Avatar of Vishnu happened in the beginning of this Kalpa. Similarly, in the beginning of this Kalpa, a Rishi named Saratwata was born which was the previous birth of Vyasa of 28th Dwaparayuga of Vaisvasvata Manvantara, because of
which this kalpa is called Saraswata Kalpa.