So, human packs tended to be unusually large for predatory omnivores, with night/morning watches. Most predators would not attack a full pack of H. sapiens unless they had numbers on their side, which few animals would besides a handful of very large packs of Hyena (Both African and Eurasian). A small pack of humans that had fallen on hard times would definitely be at higher risk but snoring in a large human pack wouldn't really be much of a risk at all. Most things that hunted us, would wait until we spread out foraging or were exploring in small enough numbers that they could overpower our numbers.

Neanderthals moved in small bands. Part of our advantage was that we tended to have bigger packs and relied on safety in numbers.