The tenancy agreement for the premises is between landlord and tenant, not between landlord and the HSE. The HSE did not rent the property, they assisted the tenant towards the cost of rent (it's not paid in full, the tenant must make a contribution too). The HSE have no obligations regarding the behaviour of tenants, as Welfarite said earlier.
If the tenant wasn't receiving rent supplement, and left the premises as described, what action would the landlord take? The fact that the tenant qualified for assistance towards the cost of rent doesn't change this situation.
It's not the job of the CWO to monitor the behaviour of tenants, other than to verify that they continue to reside at the address and have a continued entitlement to Rent Supplement.