SUMMARY:
I understand that a time off type is associated with a liability to the organization in the sense that the company is liable to pay the employees even for days when they book a time off. I would like to create a time off type with no liability associated with it. So when a user books a time off against that time off type, the company will not be liable to pay him for the time off.

RESOLUTION:
Web TimeSheet supports creation of pay codes with zero pay code multipliers associated with them. By default, Regular Time pay code is associated with a pay code multiplier of 1 and over time with a pay code multiplier of 1.5. To resolve the issue, you first need to create a new pay code and associate this pay code with a pay code multiplier of 0. Secondly, you can create a time off type by name Unpaid Time Off (or any other name of your choice) and assign the new pay code to the time off type.