2KiB is a peculiar size. Typical page size is 4KiB, and you probably want to allocate two pages - one for the stack and one for a guard page for stack overflow protection. That means that a fibers' minimal size ought to be 8KiB.
You should look into how go manages goroutines. It is indeed 2kib stacks by default without the need for guard pages. They use a different mechanism to determine overflows. Other runtimes can do similar things.
