No. They lose their benefit.
I've seen it happen. They lose their benefit and get stuck in the system for a few months. They then get threatened with evictition, have to pay unpaid rent back, regardless of whether they end up qualifying for housing benefit again at a later date, and some lose their houses because of it.

THAT is why most people end up in emergency accommodation.
( Wicca'd Witch needs ideas for a new sig on..., Tue 5 Feb 2008, 14:25, archived)

I've not seen a single person lose their JSA for more than about a fortnight
In this stage, they're propped up by emergency funding and then get income support.
( Methylene Blue - electrohead, Tue 5 Feb 2008, 14:36, archived)