Time will continue, the earth will continue, but there will be no humans on it and very few animals or fish. Mainly just bugs.
Bugs can survive most anything, especially the cockroach as they say.
However, I do not recommend that anyone wish to become a cockroach, one of the most reviled creatures on earth. One should desire to be more like the dolphins, the highest spiritually evolved creature on earth. There is no negativity in them whatsoever. Their only goal in life is to serve each other and mankind. If you observe them long enough, you will see that they are joyful and happy, most loving and caring creatures.