Yes it can. In fact this is crucial in Bayesian Analysis where we are modeling something according to some distribution but we are unsure of paramaters in it. Exactly like user158565 commented. In his case, if we want to sample from Y, we first sample a mean from $\mu$'s distribution, then using that we sample a Y by the distribution defined by this $\mu$. We can keep nesting distributions one after the other like this!
Practically these things change for a system due to natural fluctuations. Check out bayesian linear regression for a quick example. The posterior predictive distribution tries to encapsulate both these into one distribution. Otherwise Statistical Rethinking is a light book to read abit more.