According to the IRS:
Question: If you have run a small business in the past, but this year there is no income or expenses, is it necessary to file a Schedule C?
Answer: If your sole proprietorship business is inactive during the full year, it is not necessary to file a Schedule C (Form 1040) Profit or Loss from Business (Sole Proprietorship) for that year.
Please see IRS Publication 334 Tax Guide for Small Business for additional information.
Note that any link in the information above is updated each year automatically and will take you to the most recent version of the document at the time it is accessed.