An unfinished cigarette that is purposely extinguished so it can be saved and re-lit later on. Sometimes they will end up saving the day for you (hence the name safety) when you're out of cigs and craving like a madman. Example: I'm smoked out. I'm makin' a safety.
SAFETY
Meaning of SAFETY in English
Slang English vocab. Английский сленговый словарь. 2012