During a "downsizing" why wouldn't a companies give people 1-2 weeks notice beforehand so they have a chance to train other employees about what they were working on, say goodbye, etc? Severance pay is nice for finding a new job, but not for being able to keep in touch with other employees, setting up references, etc. What reasons would a company have for doing it suddenly and without warning?
If you make someone redundant you are saying their job is not needed thus there is nothing to hand over. If there was then the person being made redundant could have a legal case
Also making people redundant says the company is not doing well. Knowledge of the redundancy could affect a company's stock price (could significantly rise! or fall) this stock market rules could well mean that notice cannot be given.
However I suspect the main reason is as given in other answers that if you sack someone they could tend to take retaliatory action so best to stop the employee's ability to do that,
Aside from what's being said already by @kevincline, telling someone that they'll be laid off, then asking them to train other employees to do their job is quite absurd, they'll just tell you to screw you.
In fact, asking them to do anything productive will be most likely be met anger.
There is really no valid point in keeping an employee that you have laid off. And for an employee, there is absolutely no valid point to stay at work once they know they'll be laid off.