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Earlier this week, Southland Mayor Gary Tong announced the closing date had been extended by a month to March 14, for what he said were "timing issues'' because of the Christmas holidays.
However Belinda Burtenshaw, foster parent of Cameron Frethey who works for SDE, said the process was causing stress for employees' families.
"This is the only job that he could ever have and if he loses it will be hard for him socialise again. What it sounds like is that very few organisations want to take this job off SDE and haven't put a tender in.''
Two other family members said they were advised they would be "jeopardising'' the tender by making their concerns public.
Invercargill Ratepayer Advocacy Group spokesman Nobby Clark said he "smelt a rat''.
He believed no-one else had submitted a tender and claimed Wastenet was waiting on a late submission.
"I think the council staff took the opportunity to test the market place. This is not about getting the lowest price, it's about employment opportunity for these people.''
Southland disAbility Enterprises general manager Hamish McMurdo declined to comment on the deadline extension.
Mr Tong, who is also spokesman for the Waste Advisory Group, said he was unaware of how many tenders had been submitted.
"We are not allowed to open the tender box until the end of the process.''
He said the decision to extend tenders was made exclusively by Wastenet.
The Waste Advisory Group met in Gore on Wednesday - but the meeting was closed to the public and media.
SDE's contract is for recycling of all Gore, Invercargill and Southland councils' collections.