"Please, please forgive me. But I won't be home again"
This part signifies when they run away. They kind of say that there sorry but no-one will see the again.

"Maybe someday you'll look up
And barely conscious you'll say to no one
Isn't something missing?"
In this part they're hoping someone will miss them, and that someone will at least realize they left.

"You won't cry for my absence, I know
You forgot me long ago"
This part is they're feeling forgotten and unwanted, and they feel like nobody cares about them.

"Am I that unimportant?
Am I so insignificant?"
This part they're wondering if they really matter, and if they really are forgotten.

And then "Isn't something missing?
Isn't someone missing me?" means they left, that they're gone. They would be out on their own by then, and thinking, just thinking and surviving.