They can close the card even if there is due or emi. Because Cc doesn't directly get closed. They first put a temp debit block for a week and ask to clear whole due as a one time payment. If closure request is accepted, there will be no more emi, full remaining amount will be added to due.
But generally if you have due, they will keep it active. & even if it is closed/blocked they can reinstate the cc as long as they haven't reported it to credit bureau, which generally takes 30-45days.
What
@kshitij_0 suggested is the safest option.