A debt exists until it's repaid. If there is no communication between the lender and the debtor for 6 years (and there has been no attempt at communication, such as by the lender writing to the last-known address of the debtor) then the lender can no longer pursue the matter through court action. However the debt will continue to exist and appear on credit reference records.
In the circumstances you refer to, matters are complicated by the fact that a 16-year-old can't legally enter into a contract, so the debt probably isn't enforceable anyway. However that doesn't mean that it can't remain on a credit reference file. Further (since your boyfriend probably pretended to be at least 18 in order to take out the contract), trying to get out of paying by revealing that he was too young might be inadvisable because he'd be admitting to fraud (which can carry heavy criminal penalties).
Chris