When and why are random number generators not sampled for certain functions and their inputs?

In a previous question of mine I learned that a random number generator is not sampled when p = 1 or p = 0 in the rbinom() function. Are there any other functions one should be aware of where a random number generator is not sampled given certain inputs? The reason I ask is that the simulated output of certain variables is not constant between simulations after changes in parameters unrelated to these output variables despite the use of a fixed seed.

The version of R I am working with:

> R.version
               _                           
platform       x86_64-w64-mingw32          
arch           x86_64                      
os             mingw32                     
system         x86_64, mingw32             
status                                     
major          3                           
minor          6.1                         
year           2019                        
month          07                          
day            05                          
svn rev        76782                       
language       R                           
version.string R version 3.6.1 (2019-07-05)
nickname       Action of the Toes