If the restaurant business is run as a limited company, and goes bust, your son's chances of getting any money are almost nil. He will join a long list of creditors who can submit their claims to the receiver but bodies like HMRC are 'preferred creditors' who will probably get all of what's left, leaving nothing for the employees or other creditors. (Your son's former boss would not be liable for paying him as he is legally 'separate' from the business).
If your son's boss is a private trader, he would remain liable for paying the restaurant's bills (including employees' wages) after the closure of the business. However, you can't 'get blood out of a stone'. i.e. the trader can't pay money he hasn't got. It might be necessary for your son to pursue his former employer for his money, via the small claims track, through the courts. However, even if the court issued a judgement against the trader, it could still be difficult to get the money.
If HMRC's Minimum Wage Investigations Department found that your son had been underpaid, he would be entitled to receive the missing pay but the same problems would apply. (i.e. he would be unlikely to receive any money from a failed limited company and he might have difficulty getting it from a private trader).
Your son should be entitled to receive Job Seeker's Allowance during his search for employment. He should tell the Jobcentre Plus staff that he has been subject to 'constructive dismissal' because of the non-payment of his wages:
http://www.direct.gov.uk/en/Employment/Employe es/RedundancyAndLeavingYourJob/DG_10026696
(NB: See the information about the ACAS helpline, under 'Where to Get Help', on that page. They should be able to advise your son further).
Chris