The phrase "local death" can refer to someone who has passed away within the community or region they lived in. Some synonyms for this phrase could include "regional demise," "proximal passing," or "community loss." These phrases all highlight the idea that the death has occurred close to home, and may be more impactful for those who live in the area. Other possible synonyms could include "hometown death," "neighborhood passing," or "in-area loss." Ultimately, these phrases aim to emphasize the connection between the deceased and the people and places within their immediate vicinity.