One of science’s greatest challenges is how life can spontaneously emerge from a mixture of abiotic molecules. A complicating factor is that life is inherently unstable, and, by extension, so are its molecules—RNA and proteins are prone to hydrolysis and denaturation. For the synthesis of life or to better understand its emergence at its origin, selection mechanisms are needed for such inherently unstable molecules. Here, we present a chemically-fueled dynamic combinatorial library as a model for RNA oligomerization and deoligomerization that shines new light on selection and purification mechanisms under kinetic control. In the experiments, nucleotide oligomers can only sustain by continuous production. We find that hybridization is a powerful tool for selecting unstable molecules as it offers feedback on oligomerization and deoligomerization rates. Template-based copying can thereby select molecules of specific lengths and sequences. Moreover, we find that templation can also be used to purify libraries of oligomers. Further, template-based copying within coacervate-based protocells changes its compartment’s physical properties, like their ability to fuse. Such reciprocal coupling between information sequences and physical properties is a key step toward synthetic life.