Can you confirm the source of this narration?
إذا كثر الزنا كثر القتل ووقع الطاعون
Imam Hakim (rahimahullah) has recorded this as part of a longer narration, as the statement of Sayyiduna ‘Abdullah ibn Mas’ud (radiyallahu ‘anhu). He has declared the narration authentic and ‘Allamah Dhahabi concurs.
(Mustadrak Hakim, vol. 4 pg. 504. Also see: Fathul Bari, Hadith: 5734 for other similar Hadiths)
When adultery becomes rampant, murders and plagues will become widespread.
And Allah Ta’ala Knows best.