If I want to close my small business, will I have to pay unemployment to my employees?

You don't pay the employees unemployment--your state's department of labor does. Yes, they will be eligible for unemployment, since their employment would have been terminated without cause (e.g. without them violating policies, insubordination, excessive unauthorized absenteeism, etc.). While it would be the case that IF your business remained in operation, you would have higher assessments (payments) for unemployment down the road because of this experience, that's a non-issue if you're closing down anyway--a business that is out of business does not pay unemployment assessments.