The purpose of EOLR's is to allow the control panel to supervise the field wiring for open or short circuit conditions. How the control system responds to each depends on the system's configuration, but generally speaking, a control system views an open circuit as a fault or alarm condition, and a short circuit as an alarm condition (if armed). The EOLR's allow the panel to differentiate between the two conditions by looking for a known resistance.
An EOL resistor should always be installed at the last device and never inside the control panel. Placing resistors anywhere other than the end of the line does nothing to supervise the wiring, which is the reason for using resistors.
Fire zones usually use EOLRs. This is because fire sensors are "Normally Open" devices; they only close the circuit when they trip. Therefore, a fire zone in its normal state would appear the same to the system as one where the wire has been cut: namely, open. To prevent this, a resistor is used to close the circuit (with reduced voltage), so that it can be supervised.