The purpose of the EOL resistor is to have a set of detectors wired in series where shorting or opening the two wires causes an alarm. I don't get the need for this on a smoke alarm, but it's standard for burglar alarms: a thief can't bypass the alarm by either shorting together or opening wires. (There are still people who think that shorting means connecting two wires together and shorting means disconnecting one wire. If that's you, you're not going to understand this.)
A good answer is easier with a clear question giving the make and model of everything. "The biggest problem in communication is the illusion that it has taken place." -- G. “Bernie” Shaw
