The deal, for an undisclosed amount leaves Hyper Value - which Hilco bought 50 per cent of in August - with 15 stores in Wales and Southwest England.
Nine of Hyper Value's remaining stores are running closing down Sales at present.
A company spokeswoman said that Hilco would 'wait and see how these revenue-driving sales went', before deciding whether to close the stores, sell them or carry on trading.
Hyper Value managing director Ian Rogers said: 'The business has traded below expectations in the past few years so we have, regretfully, decided to close a number of the loss-making stores while we seek alternative strategies for the remaining business.'
There was little detail available on the buyer of the four stores, Buyology. The spokeswoman said it was a 'discount retailer'.
Buyology was registered as a business with Companies House in Cardiff on September 26 this year.
Its principal director is Bristol-based Robert Hoy, who holds directorships with another eight firms besides Buyology, ranging from hot tubs to property to van hire.
When Hilco bought the 50 per cent stake in Hyper Value it intended to invest more than£9 million in the business.
This figure was conditional on Hyper Value creditors agreeing to a deal to receive 45p for every£1 they were owed. Hilco said today that 95 per cent of these creditors had accepted the terms.