Short answer: yes, it’s generally safe, but it’s not pleasant and I’d keep your guard up.
Terminal B landside does have seating and you won’t be the only person there overnight. You’ll see other stranded travelers, airport staff, and security around. That said, it’s still LAX at night, so I wouldn’t fully relax or fall into a deep sleep, especially with multiple bags.
Arrivals vs departures doesn’t make a huge difference landside. I’d stay near departures where there’s more lighting and occasional foot traffic, then head to Terminal 6 around 4am when check in opens. The inter terminal walk is covered and well signed. At 4am it’s quiet but fine, just stick to the main paths and don’t wander.
Airport shuttles do run early, but walking between TBIT and T6 is usually faster and simpler than waiting around. With luggage it’s still manageable.
If you’re already nervous and have a lot of bags, I’ll be honest: a cheap airport hotel or even a few hours somewhere nearby would be way more comfortable. But if you’re set on staying at the airport, Terminal B is one of the better places to do it.
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