he purpose of EOLR's is to allow the control panel to supervise the field wiring for open or short circuit conditions. How the alarm responds to each depends on the panel as well as system zone programming, but generally speaking, an alarm views an open circuit as a fault or alarm condition, and a short circuit as a trouble or alarm condition (if armed). The purpose of EOLR's is to allow the panel to differentiate between the two conditions by looking for a known resistance.
EOLR's should be installed at the last device on the loop, electrically speaking, and not inside the control, unless special conditions are met. The benefits of EOLR's on protective zones with all concealed wiring is commonly argued by professional installers, as well as EOLR's installed inside the control unit, negating their effetiveness, as well as disabling the EOLR feature and using NC (normally closed) loops for zone definitions. The use of EOLR's is recommended and is particularly important when the field wiring is subject to damage or compromise.
A fire EOLR should always be installed at the last device and never inside the control or across the zone defined as fire, as this is an inherent safety issue.
Some equipment supports Double End of Line Resistors (DEOLR) to further differentiate between conditions that may exist on the loop.
I've linked my source.