Permanent random numbers (PRN) and collected random numbers (CRN) sampling are practical methods of controlling overlap between different samples. The techniques can be used for overlap control between samples for the same survey selected as different time periods or between surveys at the same time period. Although the methods are in wide use, their properties, when a population is changing due to births and deaths, have not been studied extensively. Ideally, each technique should produce a sample proportionality allocated to births and persistent units when equal probability sampling is used. We study particular PRN and CRN schemes that produce fixed size sample, involve complete, rather than partial, rotation of units within strata, and are effective at meeting the goal of coordinating two or more surveys by minimizing the overlap among them. We present theoretical and empirical results showing the circumstances where proportional allocation is approximately obtained with these particular schemes. We also discuss important cases where PRN and CRN sampling are substantially different in their coverage of birth and persistent units.