Impact of Natural Disaster on Production Function
Suppose the Cobb-Douglas production function is $Y = AK^{\alpha}L^{\beta}$, and the effect of the disaster is to reduce $K$ from $K_0$ to $K_1$. If any change in $A$ and $L$ is insignificant, then you can look at this in two ways:


Focusing on a partial production function in terms of $L$ only (that is, treating $A$ and $K_i$ as fixed parameters in the short term), there has been a change from $Y=AK_0^{\alpha}L^{\beta}$ to $Y=AK_1^{\alpha}L^{\beta}$. With $K_1&lt;K_0$, that implies a shift downwards, with labour productivity having decreased.
However, the full production function in terms of $K$ and $L$ is unchanged, and there has been a movement on the surface defined by the function. If the function were plotted in three dimensions, with $K$ and $L$ on horizontal axes and $Y$ vertical, then this would be a movement downward (and along the $K$ dimension). 


These are both valid ways of describing the situation: which is more useful would depend on what you are trying to do.

One caveat. Although production functions often suggest otherwise, labour is not homogeneous. Even if only a few people are killed, the effect on production could be significant if those people happen to have key skills that are in short supply, or knowledge the loss of which would affect the technological level.