The HUD-1 is signed so that the parties have acknowledged and agreed to the movement of money in the transaction. The settlement agent signs to certify that they have or will disburse funds as noted on the HUD-1.
The HUD-1 is a settlement statement designed to aid consumers in a federally related mortgage transaction. It is not required nor it is always used or signed in transactions that do not fall under the federal regulations.
For instance, though we use a HUD-1 in cash transactions, I would still close even if the HUD-1 was not signed. I prefer a signature but I would not require a signature.