Most of the time printers reduce the resolution in large file e.g. Billboard or something like that. What you think about that and why there reduce the resolution?

its correct, as long as original file is a high res, it make the rip (bitmap readable file for Large Format Printer) process faster, and smaller files to avoid the CPU stops at the middle of printing because the file is to heavy while send from CPU to printers

Based on my own experience, I think this might not refer to the printer.  The company I worked with doesnt have a machine to print for a billboard ads and we always take our layouts to other printing stablishments to do the job. Regarding with my illustrations, I always set my layout to a full resolution but after it was cascaded to other printing stablishments, the resolutions always changed or reduced. Basically they change the resoution of the file for the machine to load fast - based on the printing establishment. The truth is for them to save a lot with the printing. 

I used to print brochures and flyers with a high resolution and using high resolution, the printing output is not that fast but it will really cost you a lot with ink or toner.

Reason behind this is that you have not created file in exact size of billboard. if you want not to reduce you file resolution then create it in exact size in the first place. resolution will never be reduced

PS:

here size means length and width of file.