The increased public safety from your experienced relative could create other opportunities in the city, such as a thriving retail sector. Whereas without that standard of public safety, shoplifting or other petty criminal activity might drive retailers away.
You can claim that the overall demand for police officers would be one less in this scenario. However the demand for retail employment and the demand for those goods sold by retail shops might increase. Therefore, the overall size of the pie has increased. We can extrapolate a few levels from this point. A growing retail sector might necessitate further public or private security roles.
Of course as with any example, there are probably several approaches to produce gotcha counter arguments. This is only meant to illustrate the larger point and not argue the specifics of the example.
The employee could retire and collect 100% pension or they can continue to work and collect around the same amount of money as salary. If they don’t retire, then the budget hasn’t been freed up to hire the new person.
Which is the objective we seek, full employment regardless of productivity concerns or productive allocations of finite resources?
I'd suggest that productive allocations increase our living standards, which is the goal of employment itself. Full employment for the sake of employment trends towards make-work, drudgery, high costs and low quality.