According to tradition (see Rashi to bereishis 1:21), Hashem created a male and female Leviathan, but then He killed the female and salted it for the righteous. What happened to the male? Did it die sometime? When?
I am providing a source for the answer but one will need further research to better understand it.
Gemorah avodah zara 3b states that "He (the Almighty) sits and makes sport with the leviathan"
So at least we know that the male leviathan is not dead as opposed to his female counterpart.