Conundrum!!

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Tenant moved in late at night - so I agreed to give him time to read inventory and contract - (did walk round with inventory, but not in great detail)
Two weeks after moving in he has left - citing redundancy and car accident which the insurance won't cover.
We lodged the deposit, but we do not have a signed contract back so reading the small print of the My deposits it would seem the tenant has little recourse if he hasn't signed the contract.He could of course sign it if he wanted to make a claim, but then he would surely have shot himself in the foot because he would be most definitely liable for re-letting costs. However I would like to know exactly where we might stand if we refuse to return the deposit - we now have to get a new tenant, with all associated expenditure.
He has agreedto pay the rent til the end of the month - is he therfore liable for council tax?
Any ideas please?
thank you.