If this was an ordinary commercial debt (loan, overdraft, credit card etc.) then the credit check should have revealed it. However, there are 3 credit reference agencies and not all debts are logged with all 3, so you could have missed it.
If any payment has been made, or the debt acknowledged, within the last 6 years then it is not statute barred and you (& your ex if it was a joint debt) could be taken to Court and get an adverse credit record. It is also not barred if the creditor has obtained a County Court Judgement before the 6 year gap was up.
If it was a joint debt you are both liable for the whole of it, so the creditor would not have to accept any offer to pay half on the basis that they chase your ex for the rest.
It could be that the original problem arose because the account number you had was wrong and could not be tied up with the creditor's records.
If possible do not get involved in phone calls with the debt collector. Put everything in writing, send by recorded delivery & keep a copy. You could write asking them for proof of the debt on the basis that you were previously told there was not one, & also point out it is statute barred if you consider that to be the case.