Yes, Zoar was one of the five "cities of the plain" mentioned in Gen 14, along with Sodom, Gomorrah, Admah, Zeboiim. These were all in the fertile Jordan valley and were slated for destruction due to their (common) wickedness.
And it happened that in the days of Amraphel, the king of Shinar,
Arioch, the king of Ellasar, Kedorlaomer, the king of Elam, and Tidal,
the king of Goiim, made war with Bera, the king of Sodom, and Birsha,
the king of Gomorrah, Shinab, the king of Admah, and Shemeber, the
king of Zeboiim, and the king of Bela (that is, Zoar).
Gen. 14.1-2 (LEB)
According to the Babylonian Talmud, it is five miles distance from Sodom:
The Master said: “From the time the morning star appears until sunrise
a man can traverse five miles.” Whence does he adduce this? From the
passage [Gen. 19:15]: “And as the morning dawn arose, the angels urged
Lot,” etc.; and further, it is written [ibid. 23]: “The sun rose over
the earth, when Lot entered into Zoar”; and R. Hanina said: “I saw the
distance between Sodom and Zoar, and found it to be five miles.”
Rodkinson, M. L. (Trans.). (1918). The Babylonian Talmud: Original Text, Edited, Corrected, Formulated, and Translated into English (Vol. 5, p. 194). Boston, MA: The Talmud Society.
God promises to spare Zoar when Lot pleads for it, because it is a small city:
'"Behold, this city is near enough to flee there, and it is a little
one. Please, let me flee there. Is it not a little one? Then my life
shall be saved.”'
And he said to him, “Behold, I will grant this favor as well; that I
will not overthrow the city of which you have spoken. Escape there
quickly, for I cannot do this thing until you get there.”
the name of the city was called Zoar.
Genesis 19:20-22 (LEB)
Note the parallel with Abraham pleading for Sodom. But by tradition Zoar was destroyed along with the other four cities, supposedly because Lot, after begging God to spare it, didn't trust God's promise to do so and fled into the caves. Just as how God promised to spare Sodom but then destroyed it after Lot's family was removed, so according to tradition, he destroyed Zoar with the other cities of the plain after Lot left it.
Here is Josephus:
It was of old a most happy land
both for the fruits it bore and the riches of its cities, although it
be now all burnt up. It is related how, for the impiety of its
inhabitants it was burnt by lightning; in consequence of which there
are still the remainders of that divine fire; and the traces [or
shadows] of the five cities are still to be seen, as well as the ashes
growing in their fruits, which fruits have a color as if they were fit
to be eaten; but if you pluck them with your hands, they will dissolve
into smoke and ashes.
Josephus, F., & Whiston, W. (1987). The works of Josephus: complete and unabridged (p. 687). Peabody: Hendrickson."
And here is the Wisdom of Solomon, 10.6-7:
When the ungodly perished, she delivered the righteous man, who fled
from the fire which fell down upon the five cities. Of whose
wickedness even to this day the waste land that smoketh is a
testimony, and plants bearing fruit that never come to ripeness: and a
standing pillar of salt is a monument of an unbelieving soul.
The Apocrypha: King James Version. (1995)
In terms of why Lot didn't trust God to honor his promise, perhaps he was scared from the nearby destruction of the other cities. It was a sad ending for Lot, who started out so wealthy he needed to separate his flocks from Abraham, and ended up living in a cave, raped by his own daughters.