An interesting fact about the story of Jonah is revealed by the great Torah sage Rashi, who reveals that Jonah actually was swallowed by two fish, not just the One Big Fish which everyone knows about. This is learned from the midrash. Actually he was swallowed by a big male fish, spit out and reswallowed by a small pregnant female fish. I have heard this from several Rabbis and have found mention of it on the web.
http://www.ou.org/index.php/torah/article/jonah_chapter_2/Jonah's Prayer
By Rabbi Jack Abramowitz
So, there's Jonah, flopping around in the water, but G-d wasn't about to leave him like that. He sent a gigantic fish that swallowed Jonah whole. Jonah was in the stomach of the fish for three days. (The word for fish switches from "dag" to "dagah." Rashi cites a Midrash that there were two fish; a male fish expelled Jonah in favor of a female fish.) Jonah prayed to G-d, comparing the fish to the grave. Since G-d miraculously kept him alive inside the fish, Jonah knew that he would survive. He had sunk to the deepest depths, but G-d raised him up. Jonah recognized his own wrongdoing and thanked G-d for His kindness, so G-d ordered the fish to spit him out onto dry land.
http://www.hearingshofar.com/Book1.htm#_Chapter_1-13_%E2%80%93Death and Rebirth
Rosh Hashanah, the start of the New Year, is considered the birthday of the world, and the shofar blasts are compared to the cries of a newborn child (see Chapter 7 – The Ewe’s Horn). In the waning hours of the Yom Kippur, Jonah provides another reminder of the potential of spiritual rebirth, and prepares us to hear the birth cries of the ram’s horn. These ideas are expressed in the following essay:
“One answer to this question focuses on the symbolism of the belly of the fish. The fish, we recall, swallowed Jonah, after he fled G-d's call. He then remained and prayed in the belly of the fish for three days and three nights before being vomited onto land… The symbolism of three days and nights is also associated with the time it takes to travel to Sheol, the Netherworld; Jonah's descent into the fish can thus be viewed as a descent into a type of death. Furthermore, the belly of the fish directly parallels the womb of a mother. Jonah's emergence from the fish can then be seen as a type of rebirth. After traveling to Sheol, Jonah repents and is then resurrected.
“This symbolism of death and rebirth appears in many of the customs associated with Yom Kippur… Is this…fast perhaps an attempt to simulate death? …Finally, when the Yom Kippur fast ends, we reenter the physical world with the blasting of a ram's horn, the simplest sound known to ancient man. Perhaps this shofar blast should be seen as parallel to the cry of a baby exiting the womb and emerging into the world.
“This explains why the story of Jonah in the fish's belly figures so prominently in the Yom Kippur liturgy, as the story teaches us that true repentance is accompanied by a metaphysical rebirth. And indeed, when true repentance occurs, like a newborn baby, our potential is infinite.”[453]
Augmenting the theme of birth in Jonah is the midrash explaining that Jonah was in the belly of a pregnant fish.[454]
The fish that swallowed Jonah is masculine in its Hebrew gender – “dag,” but the fish in whose belly Jonah finally prayed for relief is feminine – “dagah.” The midrash explains this discrepancy by suggesting that Jonah was too comfortable in the spacious interior of the male fish to feel the urge to repent. G-d had the male fish regurgitate Jonah and, in turn, a female fish swallow the prophet. The female fish is pregnant with thousands of tiny fish inside her waiting to be hatched. In this crowded environment, Jonah feels himself in the tight space of the pit; the confinement that precedes deliverance. Prayers are squeezed out of Jonah like shofar blasts are squeezed out of the belly of a shofarist. For then every ba’al tekiah knows the truth of Jonah’s song:
“In my trouble, I called to the Lord,
And he answered me’
From the belly of Shoel I cried out,
And You heard my voice.”[455]