The phrase "fall into decay" refers to a process in which something gradually deteriorates or loses its quality over time. Synonyms for this phrase include "deteriorate," "degenerate," "dwindle," "decline," "wither," "rot," "decompose," "crumble," "perish," "waste away," "dilapidate," and "wear out." These synonyms can be used depending on the context, such as a building, a relationship, or a person's health. Regardless of the word used, they all convey the same message: something is no longer in its optimal state and is gradually losing its quality, leaving it weakened, damaged, or perhaps even irreparable.