I can only refer to my experience of the rules about 7 years ago, which, granted, may have changed since then.
I used to be a landlord and was asked by the council to repay money that they had overpaid in housing benefit to me on behalf of one of my tenants, which meant I had to recover that money back from him. When the housing benefit is paid directly to you as a lanlord you have to sign, agreeing that you will return any money overpaid.
If the housing benefit was not paid directly to the landlord, then they will not be asked to repay it. If it was paid directly to the landlord, they may well be asked to pay it back. Of course the tenant would still be prosecuted, not the landlord. It's the tenant who is making the fraudulent claim, not the landlord.