Thank you for the additional information.
Resigning typically makes it very difficult to collect unemployment benefits unless the employer is giving you an ultimatum to quit or be fired, OR if you can prove that the working conditions were so poor that a reasonable person would have been compelled to quit (the constructive discharge doctrine).
The burden is on the employee if they resign though to prove that they exhausted all other alternatives. Therefore, it is normally recommended that the employee be terminated involuntarily without good cause in order to collect unemployment benefits.
If it is feasible, the employer could be approached with regard to terminating the employee, not challenging the employee's right to benefits, in exchange for the employee agreeing to waive any claims they may have against the employer.
It does not appear the employee would have an age claim against the employee where the employer seems to be motivated by other factors in attempting to force the employee out. However, the employer may be concerned that the employee will file an age discrimination case anyway. So if the employee waives such claims in return for the employer's cooperation in seeking unemployment benefits, both parties may be able to obtain the result they are seeking.
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