The end of this book is sad. Here are a few reasons why.
Throughout the book, we've been shuttling back and forth between the present tense (David, alone in his room in the south of France) and the past (David with Giovanni and then with Hella). In the first case, David is doing relatively little. He's drinking and feeling depressed and talking with the caretaker. The second case is where we learn what happened.
What happened is tragic. Though we didn't know the details in the beginning, David announces that today is the day that Giovanni will be executed. After that, no matter what happened, the story has the air of tragedy: we know that things are going to end badly.
Now at the close of the book, very little has changed except that we, the reader, now know David's story. Giovanni is going to be executed, or perhaps already has been. Hella has left David and it is unclear if she'll ever be able to have a normal relationship again. What's so sad is that all this has already happened. David is left alone, drinking and tormenting himself, but there is nothing that he can do.
Where does that leave us? Quite simply, it leaves us wondering whether or not David is going to be OK. He has been forced to admit that he is gay; the fact that he couldn't before has had disastrous consequences. What we now want to know is whether or not he can ever be happy again, whether he can ever lift the sense of guilt from his shoulders.
Of course, the story is told by David in the present tense. David doesn't know whether or not he will be all right, so what he gives us is a last scene, and if we're curious about David's fate, we have to scour the details of the scene for hints.
To recap, here's the scene: we see David walking out to meet the bus. He says, "the morning weighs on my shoulders with the dreadful weight of hope" (2.5.150). A moment later, David decides to tear up Jacques's letter telling him when Giovanni will be executed without even opening it. He scatters the pieces to the wind.
We see that David may feel absolutely awful, but he is not entirely without hope, and he is willing to try to overcome his guilt about Giovanni by tearing up the envelope. The last detail, though, is that the wind blows some of the pieces of the envelope back against him. The physical detail leaves us very uncertain as to David's fate. Though he has not completely given up, it is not clear whether or not he will escape his guilt.