Plasmid acquisition is an important mechanism of rapid adaptation and niche expansion in prokaryotes. Positive selection for plasmid-coded functions is a major driver of plasmid evolution, while plasmids that do not confer a selective advantage are considered costly and expected to go extinct. Yet, plasmids are ubiquitous in nature, and their persistence remains an evolutionary paradox. Here, we demonstrate that non-mobile plasmids persist over evolutionary timescales without selection for the plasmid function. Evolving a minimal plasmid encoding for antibiotics resistance in Escherichia coli, we discover that plasmid stability emerges in the absence of antibiotics and that plasmid loss is determined by transcription-replication conflicts. We further find that environmental conditions modulate these conflicts and plasmid persistence. Silencing the transcription of the resistance gene results in stable plasmids that become fixed in the population. Evolution of plasmid stability under non-selective conditions provides an evolutionary explanation for the ubiquity of plasmids in nature.