I think this deserves some clarification. First, the article is about an employee being laid off in the UK, some years ago. In such a case (certainly back then, I'm not familiar with present day UK employment law but afaik it hasn't changed significantly), he would have received payment in lieu of notice (at least), and any such payment would also not be taxed. So at least in that particular case the situation you're describing where someone all of a sudden has no income would not have occurred.
Now, in the US there is a concept of "at will employment", but it doesn't in reality mean what you're alluding to either. IANAL but it roughly means "employees don't get to jerk employers around with random frivolous lawsuits relating to termination". In essence it means that, legally, employers do not need a reason to fire someone. It does not however in practice mean that employers randomly fire people all of a sudden with no payment beyond today, as you imply.
Perhaps for low-end jobs something like what you are worried about happens in the US, but I suspect it happens in the UK too. Certainly in my experience working in the UK then US, and now being an employer in the US, employment conditions as a practical matter are very similar. The major difference I could point to is that in the UK redundancy payments are tax-free. They aren't in the US. I suppose the other difference is that in the UK employees in technical fields tend to have quite long notice periods vs the US. Here, in theory it is possible to depart one job and be working at a new one a few days later.
I'm referencing the UK here because a) the article is about someone in the UK and b) I know about that jurisdiction and the US (only).