Both employee and system administrator will be able to add the contact information for "In case of emergency call".
The "In case of emergency call" information is not shared among coworkers as default. It's only shared with the employee himself and any given system administrators.
To make "In case of emergency call" visible for all in the People menu, you can activate this under:
Setup admin > Company > GDPR compliance settings >
mark Set "In case of emergency" phone number visible in People and then click Save.
Employees who have "In case of emergency call" information filled out on their BitaBIZ profile, will have an ambulance icon added in People.
Mouse over the icon to see details: