Here is a brief list of your traveling options according to security status:
Players with -2.0 or worse will be attacked in 1.0 systems Players with -2.5 or worse will be attacked in 0.9 systems Players with -3.0 or worse will be attacked in 0.8 systems Players with -3.5 or worse will be attacked in 0.7 systems Players with -4.0 or worse will be attacked in 0.6 systems Players with -4.5 or worse will be attacked in 0.5 systems
Once your security status reaches -5 you are considered an outlaw and can be attacked by players anywhere without CONCORD intervention.