For an open-ended contract either party may end it after notifying the other: at least three months for monthly-paid workers and at least one month for others (art. 44). A party who fails to observe the notice period must pay compensation in lieu of notice equal to the worker's wage for that period (art. 44).
If the employer gives notice, the worker is entitled to be absent one full day per week, or eight hours during the week, to look for other work, with pay, provided the employer is notified at least a day in advance (art. 44). The employer may release the worker from duty during the notice period while still counting service as continuous and paying the wage for it (art. 44).
The employer may not use the right to terminate while the worker is on any leave provided by law (art. 45), and may not end service without justification or on grounds of sex, origin, or religion (art. 46).
This is general legal information, not legal advice. For advice on your specific situation, consult a lawyer licensed in Kuwait.