Can anybody please tell me if it is legal for an employer to stop offering sick or annual leave when there are employees within the company that still have unused leave available to them?

For example: Can they post a notice saying effective immediately there will be no longer be sick or annual leave available to employees?

With limited exceptions, yes, they can. There is no law in any state that requires an employer to provide sick leave or any other form of leave, including vacation. In your state, it IS legal for them to have a policy in which you lose time you've already accrued.

If no sick leave is available, then EXEMPT employees cannot have their salary docked for missing time due to illness. Non-exempt employees do not have to be paid for any time they do not work.

If FMLA applies, the employer MUST allow time off for FMLA-related issues.