There are various synonyms for the phrase "allow to decay." Some of these include "let rot," "leave to spoil," "permit deterioration," "facilitate putrefaction," "enable decomposition," "sustain disintegration," and "tolerate corrosion." These synonyms convey the notion of neglect or indifference towards an object or entity, resulting in its gradual degradation or ruin. They imply an intentional or unintentional omission of action, where a lack of care or attention leads to the natural process of decay taking place. It is important to note that allowing something to decay can result in negative consequences, such as environmental pollution or health hazards.