Think about that at 1,000-person-layoff scale. If we apply some basic Little's Law math to the process here, we quickly see how "by-hand" firings would drag on for quite some time, perhaps needlessly prolonging the inevitable, and almost certainly disrupting work at the entire office for days on end.
There is no "good" way to do this. I've never had to do it myself, and I can only hope I never have to. The thought of how "best" to do it would keep me up for weeks. At the very least, I suppose in-person messengers are better than automated voicemail recordings, or sealed envelopes. But even if using a human messenger, a mass layoff is not going to go down well for the people being laid off. There is something to be said for ripping off the band-aid (though perhaps in timed batches, so you're not just dumping N people out into the cold, to fight over the same jobs on the market all at once).