Every state has a safe haven law and my google searches didn't return a single GIS application (in the US) to support these laws.
It would be great for someone that needs to stand up a quick response (maybe to a changing law) to have a template to work from. The Near Me/Near By instant app or ExB widgets are easy to set up and they might be a good fit; just looking for an application that can quickly pin point the closest drop off location and provide some basic information to someone that may be in crisis.
A survey that would allow sites to opt in (or out; maybe it's a rural location that isn't staffed 24/7) would be helpful. A Hub site and community accounts could be used to help keep the survey secure and allow sites to input and update information (contact or hours) as needed.