usually prices dont go down. the cost does relative to inflation. what usually happens is a new investor will do the analysis and build new units that are even more expensive but only slightly. now all the current tenants that can afford it will leave the current landlords and the current landlords wont be able to increase prices because there is a better product at that price level.
It does depend on where you are and how elastic supply is. In Austin for example there has been a recent decrease in rent (even relative to inflation) despite continually growing demand.
austin had such an insane explosion of supply. but they also have a price explosion just a couple years ago. probably going to see something similar with respect to GPU rentals in a couple years