It follows criticism of the SRU following the 12, 000 attendance for the game against Romania.
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And the departing chairman is disappointed at the way the SRU has been conducting its business.
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Andy Irvine, Andy Nicol, Gordon Bulloch, SRU chair Alan Munro and Gordon McKie will choose Hadden's successor.
The club was disbanded in May when the SRU decided it had little chance of becoming self-sufficient.
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Andy Irvine, Andy Nicol, Gordon Bulloch, SRU chair Alan Munro and McKie will choose Frank Hadden's successor.
In a statement, the SRU said it was powerless to prevent players accepting more lucrative offers elsewhere.
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The SRU's chief executive insisted that his organisation should not be accused of penny-pinching when considering who to appoint.
With Edinburgh now an independent franchise, Glasgow will benefit from increased SRU funding.
BBC: SPORT | Rugby Union | Scottish | SRU reveal smaller debt figures
The SRU, at that time, refused to confirm or deny that a decision had already been made to sack Williams.
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At the time of the Borders' closure, the SRU were five years into a 20-year rental agreement for the club's home stadium.
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The SRU were equally tight-lipped, stating only that the meeting had been unsatisfactory and confirming that they might look into invoking IRB regulation nine.
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"Andy was the outstanding candidate from a quite exceptional shortlist which underlines the allure of coaching the Scotland team, " he told the SRU's Web site.
And SRU chief executive Gordon McKie has thrown his weight behind a joint bid from the four home nations to host the 2015 and 2019 events.
The body is chaired by Event Scotland and features representatives from the SRU, the Scottish Executive, Scottish Enterprise, Edinburgh city council, Glasgow City Marketing Bureau and sportscotland.
EventScotland chief executive David Williams was pleased to have helped in negotiations in bring the event to Murrayfield and promised to continue working with the SRU to make the event a success.
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