If your establishment is not working on Sunday, then why should this person only come to your office and work? Let him also take off and remain at home.
Now if your question is like, if a person has not worked on a day in a week, whether he will get paid weekly off or not, then the answer would have been different.
If he is a regular employee and he has taken leave (with pay), then that day will be considered as working day and as such he will be entitled to weekly off at the end of 6 days (of working).
If he is a daily rated employee and has taken leave without pay, then he will not get paid weekly off if he has not worked for 6 days in a week.
Now, if the wages that you pay per day is one which is derived by dividing the monthly wages by 26, then the daily rate is presumed to have an element of weekly wages and therefore, for such daily rated workers, weekly off can be without pay.
What the law states is that you should not allow a person to work for more than 10 days continuously without giving him a day of rest. Also you are required to give rest after 6 days working. Nowhere it is mentioned that the off day should be paid day.
The minimum wages notifications usually contain that the wages of daily rated workers should be calculated by dividing the monthly wage by 26 and this is ensure payment for the weekly off day.