In force of mortality, one divides the probability of failure in a time interval $(x, x+\Delta x)$ by $\Delta x$. Apparently, this gives an annualised instantaneous rate of failure.
In this article, a post says "If we divide this by h (in our case, $\Delta x$), we get the annual rate at which the person is dying over that single day."
Paraphrasing the example provided there: If the probability of death for an individual over one day is $0.00004$, then the annual rate at which the individual dies is $\frac{0.00004}{1/365}=0.0146$ pa.
I don't quite understand the units for this rate. Is it "Number of deaths / year"? Because I'm not sure how probability divided by time leads to such a rate. Or is it a different type of rate?
The dimensions are probability per time.
The units are $year^{-1}$, but could have been expressed in other units of time.
It is not number per year, but probability per year. If you multiply by the size of the population, you get number per year.