We've just played a game of Fluxx, where the following occurred. There was a Draw3 and a Poor Bonus in play, so this player got to draw 4 cards. He then removed the Poor Bonus and changed the Draw3 to Draw4.
Option A: Since he raised the number of drawn cards, he needed to draw an extra.
Option B: Since the resulting rules require 4 drawn cards and he already had drawn that many he did not need to draw another.
So which one is it?
Option A, the player should draw an extra card. Here's why: The Poor Bonus happens at the start of a player's turn. Since the player already drew for Poor Bonus, and removed the Poor Bonus after the draw, that card is fully resolved. But the Draw X cards always say to draw extra cards during a turn, so the player would need to draw one more card to meet that rule change.
I would say option A. The card drawn from poor bonus is described as an "extra card", so I don't think you would think of it as "poor bonus is in play, so for me, draw 4 is really draw 5." Rather, it's "draw 4, then draw an extra card".
However, I do not believe this is something that is specifically addressed in the rules, so you would either need to email Looney Labs for an official answer, or decide what makes the most sense for you when playing.
Draw 3 was changed to Draw 4 during his turn, therefore, he should draw an extra card. Poor Bonus would not affect this. Poor Bonus gives him an extra card, not affecting the normal Draw amount.
