A long time ago, when I was a young and broke lad, I was an EMT and stationed for a bit in the Marlboro/Hudson area. At the time there was quite a bit of drug use and a few sober/recovery houses in the area. There was an occasional wellness check we were asked to "stand by" for. One in particular one had the local PD convinced her sister had done herself in (or was in the process of) because she was not answering the phone (cell phones not affordable for most at the time). The cops knocked loud and often for about 3-4 minutes. The the local FD showed up with a battering ram....door was opened pretty quick. Apartment was empty...walked in with my partner...made sure there was no body anywhere. Noticed Bills and collection notice strewn about the house. There maybe 15 minutes.
No idea, if she walked, drove, caught a ride, or did an overnight somewhere....but the place was empty.
So yeah, they can and will break down the door if someone convinces them you are in danger or dead