There are pretty strict legal limits (in the US at least) over how long a driver can be on the road without taking a break.
In fact, unless they only hire owner-operators, falling asleep at the wheel and causing an accident will almost certainly jack up the company's insurance rates, much worse than them running behind an overly tight schedule.
An abusive trucking company can accuse their drivers of steeling trucks or cargo when they're behind schedule. I've never heard of that happening, but I don't doubt the poster who said it does. It's too bad we don't come down harder on those who make such bad faith accusations of steeling.
Either the driver has a right to be in the truck, at the location he is at, or not. If he does, the police don't care, because there is no crime. If he doesn't, that is theft.
If it is theft, they don't let the driver drive on with a promise to behave; the truck (and all the goods in it) get impounded to be claimed by the company and the driver gets hauled off to jail. That would be a way worse outcome for the company.