The phrase "allow to decline" refers to the act of letting something deteriorate or weaken without intervention. There are several synonyms for this term, including "permit to fade," "enable to deteriorate," "facilitate the decline of," and "authorize to weaken." Other related terms may include "encourage deterioration," "tolerate weakening," and "support the decline." These synonyms all share the common theme of allowing or permitting a process of decline to take place, rather than actively trying to prevent or reverse it. This could be used in reference to physical objects, interpersonal relationships, or even a person's health or well-being.