Question regarding APIC-EM cluster. Running APIC-EM on 3 servers cluster, If two of the servers is been shutdown, Will the system work on one server.
No. due to "split brain" concerns. This is a standard practise with clustering. You always need more than N/2 members to be active.
In multi-host environment, different services might be running on different servers (underlying hosts). If you shut the host off, corresponding services running on it would go down as well. If at the granularity of services, if you're ok shutting down certain services, you can do so using controller Development management page, instead of shutting down the host/s altogether. For certain apps (e.g. iWAN), you may not be aware of other infra level services it depends on.
We have documented this: Cisco Application Policy Infrastructure Controller Enterprise Module Deployment Guide, Release 1.3.x - Cisco APIC-EM M…
A multi-host cluster comprised of 3 hosts is able to tolerate the loss of one of the hosts and supports a single fail-over (although with only two hosts, there is only software high availability, but no hardware high availability).