What usually happens with stock/ESOP provided to employees, if the company does not go public but employees have stock options which they bought when exited the company?

It depends on the company policy. Possible ways could be.

  1. Company buy back the shares at the time of exit with the current share value.
  2. Shares will remain with the employees and will be paid out once the company goes public.
  3. An investor can buy these shares during a funding round.

Point to note: If the ESOP are vested then employee will be fully entitled to hold the shares even after exit.