The FI indicator is basically like the check engine light you often see on cars. The ECM sets it when it receives no signal or a signal reading outside the range it expects from one of it's sensors. For both the 400 and the 650 those sensors monitor the fuel injection and ignition systems. For the 650 they also monitor the ECVT.
Just because you get an FI indicator does not necessarily mean you have a problem in one of those systems. It might just be telling you that a sensor is going bad or that a wire to a sensor has come loose.
You can determine which sensor the ECM has detected a problem with by putting the ECM in dealer mode. You do that by completing the connection between two wires on a plug that leads to the ECM. Suzuki sells a switch you can put in that plug to trip and complete the connection. Or you can just jumper between two pins in the plug with a piece of wire and complete the connection.
Once you do that a code will appear on the dash. You can look that code up in a service manual to determine where the ECM thinks there is a problem. The service manual will also give you the steps you need to go through to trouble shoot the sensor that is causing the problem.
Not all FI codes will cause the bike to stop running. With some of them the bike will continue to run with no apparent change. With others the ECM will put the bike in limp mode and you will be able to proceed but with limited performance. With others the ECM will not even allow the bike to start.
We really need to know what kind of Burgman you have to be able to tell you how the access the plug to put the ECM in dealer mode. It is located in different places on the 400 and the 650.