In SR4, 'Erased' basically removes any negative information on you - stuff that'd be useful to track you down, a bad credit report, an arrest record, that sort of thing. (It could potentially result in you getting arrested and thrown in prison, then all records being lost - meaning they have you, but they don't know why.) Having a SIN is a double-edged sword, but Erased wouldn't take it out, at least not without paying the Karma cost to remove the NQ. The reasoning behind Erased, however, is that either you have someone relatively friendly scrubbing your data-trail for you - a free sprite, a team of hackers, whatever - or for some reason info on you just slips through the cracks.
In SR5, 'Erased' removes all information it can get its hands on, but only for as long as you make the effort to lay low. If you make your profile stick up too high, the individual(s) working on keeping info on you lost have a very, very, very difficult job to do. The quality gives examples - holding onto a false ID for more than three months (which would then start to develop your actual profile), living above a Medium lifestyle for a month or more, that sort of thing. Getting/having a SIN is the ultimate in 'my profile is sticking up' - someone, somewhere, has records of the real information on you, from retinal, voice, and fingerprints to a genetic scan. Getting rid of a SIN is a tough thing to do; consider the karma cost of removing the NQ. This very protected chunk of information starts to collect linkages, ones that can't be easily erased as long as the SIN exists; it's the equivalent, so to speak, of a Rating 20 Fake SIN, and it's not something of which you can just dump and buy a new one. So there's a tough-to-break link, one which over time makes you just as if not more traceable as the next 'runner - which thus eliminates the effect of 'Erased'.
