>>>gets a dbs check done on them?
The only people who have access to DBS checks are employers and voluntary bodies who are considering taking on a new employee/volunteer in a role associated with the administration of justice or which involves regular contact with children or vulnerable adults. Absolutely nobody else can access DBS checks and anyone who attempts to do so will be committing a serious criminal offence. (You can't even get a DBS check on ourself. Even police officers' access to criminal records is restricted on a 'need to know' basis. A police sergeant was found to have checked up on the criminal record of his daughter's boyfriend. He was sacked, prosecuted and sentenced to 2 years imprisonment).
Similarly, the Data Protection Act prohibits anyone from creating a private database of criminal records. (Newspapers have to take care to remove details of court cases from their websites after a fairly short period of time in order to ensure that they don't effectively create such a database).
If you've already had a background check carried out (with it appearing to show that the person doesn't exist) then all you can do is either to reject the tenancy application or to simply ask the applicant to show you some additional ID. For example you could ask him, without prior warning, to open his wallet and show you his bank cards. (Anyone who's got a debit or credit card would normally show up on a background check unless, possibly, he's never applied for credit or had a mobile phone account).
>>>I have a sneaky suspicion that this person has been in trouble with the law before
Given that over a third of British men acquire a criminal record before the age of 30, that would hardly be surprising! Surely you're not really suggesting that they should all be denied the right to rent housing for the rest of their lives, are you?