While LFT functions as an important character in the novel, he is also a symbol of the coming age. And judging by what LFT does, Hardy does not have high hopes for the safety and security we will find in the twentieth century.
We get into Little Father Time's social significance in greater detail in our "Character Analysis," so here, we will just point out that Little Father Time's actions (killing himself and the children) are shocking to everyone except for the doctor that Jude and Sue call in. Sue blames herself for the deaths of the children, but the doctor is quick to point out that 'it was in his nature to do it…it is the beginning of the coming universal wish not to live' (6.2.43).
In other words, none of this is LFT's fault. He's not a bad kid; it's just "in his nature" to take a deeply dark view of the world around him. With the doctor's diagnosis, the novel implies that, if the social circumstances of class injustice and poverty don't change, the world is going to grow so horrible that there will be a "universal wish not to live."
According to this logic, Jude's suicidal misery by the end of the book is the beginning and not the end. Things are growing so grim and difficult that, some day, no one will be able to bear the cruelties of living in the modern world. Clearly, Thomas Hardy is about as far from optimistic as it's possible to get. Jude the Obscure is not a book to read if you're feeling at all depressed or unhappy about the future.