Just for piece of mind on this for the future...
Assuming 1734 Point I/O modules local to a CompactLogix 5370 L1 controller -
The 1734 Point Bus fully supports RIUP (Removal and Insertion Under Power). As the CompactLogix 5370 L1 controllers use an embedded Point Bus, they too fully support RIUP. This, of course, is just deeming it safe to remove and insert the modules while there is power on the controller and backplane. RIUP does not take into account what happens the status of the system. It just means you are not going to damage any components while doing so.
For the status during RIUP, we can do as Ken has advised and either choose to ignore the connection loss to a particular module while it is removed, preventing a controller fault, or we can inhibit the module.
For the Point Bus backplane during RIUP - we must remember that many standard Point I/O modules are added to the backplane using one or other of a Terminal Base Assembly (1734-TBx, -TOPx, etc.). When we remove a module from these bases the backplane is still intact through the base unit. The modules themselves are not needed to maintain the backplane connection.
If it's suspected a base itself is faulty and you wish to replace the base as well, then yes, the backplane will be broken once you remove the base from the middle of a Point Bus. However, if the module/base you wish to remove is at the end of a Point Bus, then you may remove them both without affecting any remaining modules to the left. As we know, there is no End Cap termination for the Point Bus. It is just a plastic protection cap. So removing anything from the end has no effect on the rest of the backplane.
These removals I'm describing as having no effect are again just in relation to not damaging any components or affecting the backplane. You still have to manage what happens the status of the controller when doing so.
Regards,
George