Does a fall in the wage rate always reduce hours worked? In the Neoclassical Labor-Leisure model, does a fall in the wage rate always reduce hours worked?

Or does it depend on whether the substitution or income effect dominates?
It is more common to consider an increase in the wage rate: in that case, assuming leisure is a normal good, the income effect should increase leisure (more money available to pay for it, making it more affordable) and the substitution effect should reduce leisure (each hour worked brings greater benefit than before the increase, encouraging work), with a net effect which could go either way

So with a reduction is the wage rate, you can simply reverse this: assuming leisure is a normal good, the income effect should reduce leisure (less money available to pay for it, making it less affordable) and the substitution effect should increase leisure (each hour worked brings less benefit than before the reduction, discouraging work), with a net effect which could go either way

In the improbable situation that leisure were an inferior good, the income and substitution effects would work in the same directions, so a wage rate increase would lead to less leisure and a wage rate reduction would lead to more leisure