From SR page 62
"Characters with Magic or Resonance attributes are subject to penalties if they have an Essence lower than 6. For each point or partial point of Essence below 6, the character loses 1 full point from her Magic or Resonance and the maximum for that attribute is reduced by 1. The maximum rating for Magic is 6 + initiation grade (see Initiation, p. 189); for Resonance the maximum rating is 6 + submersion grade (see Submersion, p. 238)."
From SR page 189
"A character’s initiate grade cannot exceed her Magic attribute. If a character’s Magic is reduced below her initiate grade, she loses that level of initiation and the metamagic she gained with it."
I just want to make sure I am not missing something in the math here.
Lets say we have a character Joe Schmuckatellie. And poor Joe has an Essence of 1 and Magic of 1, for whatever reason. (Formally having a Magic and Essence of 6 and then running into the vampire hooker, or being a cybermonkey with Latent Awakening, ect ect)
Now, Joe initiates to grade 1. His new Magic maximum is 2 (Essence 1 + initiation grade 1). Joe spends karma to raise his Magic to a 2.
Since his Magic is now a 2. He can now eligible to buy a grade 2 Initiation.
Joe initiates to grade 2. His new Magic maximum is 3 (Essence 1 + initiation grade 2). Joe spends karma to raise his Magic to a 3.
Since his Magic is now a 3. He can now eligible to buy a grade 3 Initiation.
Rinse, repeat.
Given these conditions, an Essence 1 character has no real limit on his Initiation Grade or Magic, as long as he has time and karma.
If he saves up his money along the way, he could even get that nasty essence loss fixed, to avoid said hooker coming back and using his one remaining essense like a Sip-Up.