The Tanakh says Jonah cried out from Sheol which is the grave and chapter 2 shows he basically drowns but before dying or his soul fainting he cried out in his mind to God. After this event God sends the fish to protect Jonah's body for 3 days.
That just took it out of the over simplified phase. Interesting.
But?
Looks like he was swallowed alive.
Jonah 2:1-7
1
From inside the fish Jonah prayed to the Lord his God.
2 He said: “In my distress I called to the Lord,
and he answered me.
From deep in the realm of the dead I called for help,
and you listened to my cry.
3 You hurled me into the depths,
into the very heart of the seas,
and the currents swirled about me;
all your waves and breakers
swept over me.
4 I said, ‘I have been banished
from your sight;
yet I will look again
toward your holy temple.’
5 The engulfing waters threatened me,
the deep surrounded me;
seaweed was wrapped around my head.
6 To the roots of the mountains I sank down;
the earth beneath barred me in forever.
But you, Lord my God,
brought my life up from the pit.
7 “When my life was ebbing away,
I remembered you, Lord,
and my prayer rose to you,
to your holy temple.
