Why does it say that Hashem will send down to "Be'er Shachas"?
Radak: He will send these betrayers to Gehinom. Their Nefesh will die when their bodies die.
Malbim: He will not kill them; they will kill themselves 1 . Killing himself shows that he wanted to divide his days in half - half in this world, and half in the world to come. This will not be. Hashem will send them to Gehinom, so they will not merit the world to come.
Other than Achitofel, who else killed himself? Chazal say that Do'eg was the Ger Amaleki whose mouth caused his own death (refer to 52:6:2:2). We expound this verse to discuss also Do'eg (refer to 55:24:2:1*), and also he is listed among those who have no share in the world to come (Sanhedrin 90a). (PF)
What is the meaning of "Lo Yechetzu Yemeihem"?
Radak: Also their bodies will die via Kares; they will not live half their lives 1 , for they did not fear You.
Malbim: Refer to 55:24:1:2.
Sanhedrin 69b: Do'eg lived only 34 years, and Achitofel only 33. A normal life is 70 years (90:10). Sanhedrin 106b applies the verse to Bil'am; he lived 33 years.
For what does David trust in Hashem?
Radak: You will save me from them, complete my days and establish my kingship.