The directors resigned at the end of last season after the club was relegated and spiralled into debt.
According to a High Court writ, they gave personal guarantees of £250,000, which gave the club time to settle a £757,408 debt owed to Mowlem for a year's work on the Ivor Doble Stand. Work on the project halted in 2001.
The seven are former chief executive Bernard Frowd, ex-owner Ivor Doble, and directors Peter Carter, IM Couch, Stuart Dawe, Peter Dobson and Joe Gadston. Mowlem is suing Doble for £40,000 and the other six for £35,000.
The club failed to make scheduled payments to reduce the debt to Mowlem, and by 31 May this year it still owed the company £514,876. Mowlem then wrote to the guarantors demanding the money, but this was not forthcoming.
The firm met club representatives and creditors last week at a crisis meeting to determine the club's future. It was agreed to enter into a corporate voluntary agreement whereby creditors would receive 10 pence in the pound.
A Mowlem spokesperson said: "We entered into the agreement with the club as we were anxious not to push them over the edge."
The club is now run as an "industrial provident society", a charitable trust owned by the supporters and supported by their membership contributions. The Exeter City FC Supporters Trust owns 63% of the club. The chairman is local businessman and supporter Ian Huxham.
Work on the Ivor Doble stand commenced in 2000 but stopped following year after interim payments halted. Supporters can watch games but tonnes of rubble have been left under the stand, rather than the facilities planned.
Mowlem would not discuss the case against the seven directors in detail, but confirmed that discussions were continuing.
Huxham said: "Nobody at the club is proud of the fact that creditors have been asked to settle for 10% of what is due. However, most people will understand the debt was not of our making. We will leave Mowlem and the previous directors to discuss their arrangements, while we ensure our obligations to the arrangement reached with Mowlem are fulfilled."