Former Cosatu general secretary Zwelinzima Vavi and EFF leader Julius Malema are plotting to overthr.
At least 140 employees in the IT department will lose their jobs, Solidarity said in a statement.
The trade union says it is in possession of evidence that other departments will also be affected by retrenchments, but Absa is keeping mum on how many people will be retrenched.
"We are astounded by the callousness with which Absa is carrying out the process.
"First, employees were forced to pack up their belongings and escorted out of Absa's offices. They were sent home for three months for so-called gardening leave and were told that other positions would be sought for them in the company.
"Now they are getting retrenched by e-mail," Dirk Hermann, Deputy General Secretary of Solidarity, said in the statement.
In the letter to the employees, they are requested to complete a form whereby they resign from Absa, the union says. The form's heading reads: "Notice of termination of service". Employees have to complete the date of their resignation on the form.
"If employees complete and sign this form, then it is no longer a case of retrenchment, but of resignation. The employees will therefore not be entitled to severance pay or unemployment insurance.
"From a legal perspective the implication is that someone who worked for Absa for 40 years will be walking away without a cent," Hermann said.
Solidarity called on employees not to complete the form.
Time-line of events as provided by Solidarity:
- On 7 May 2012 at 15:20, employees received a letter by e-mail informing them that attempts to place them in other positions had been unsuccessful.
- On 8 May they were requested to complete forms to resign from their medical aid and pension and a form to resign from the company in order to ensure a seamless exit from the bank. They must also hand in all property of the employer that may still be in their possession.
"In effect, the employees find themselves in a position where 'today' they are told that 'tomorrow' they have to say 'goodbye'," Hermann said.
In the letter's closing, the employees are thanked for their valuable contribution in Absa and wished success for the future, Solidarity says.