Suppose it’s a Draw 5, Play 1 type of situation and no one plays a Hand Limit or a multiple Play rule. Eventually everyone has a big hand and the draw pile runs out. The discard pile gets reshuffled and reused, but suppose the situation continues until there are no cards left to be drawn. What happens? Do you just skip the draw phase of your turn till your next turn comes up where you can draw enough cards for the ‘draw requirement’? or draw what you can now and proceed to your turn?
A: Draw what you can and continue. In general, if the rules command you to do something impossible, then you just do as much as you can, and move on. If the rule says Play 3 and you only have 2 cards, then you Play 2 and stop. Similarly, if the rule says Draw 4 and there are only 3 cards for you to draw (even after reshuffling) then you draw 3 cards and proceed with the Play phase.
So yes, if the Draw pile and the Discard pile are both empty for someone, you just continue with some people not getting any new cards during their Draw phase. Now, some cards might enter the discard pile during a person’s turn, but they don’t get to immediately Draw those available cards retroactively. You don’t assess whether the discard pile needs to be reshuffled until there is an actual need for someone to Draw. Mind you, you’ll all find yourselves drawing things someone else just played for a while, but you might not choose to use them right away.
In such a situation everyone will be holding massive hands of cards so there should be plenty you can Play, even if you’re not drawing any. At some point someone will play a Hand Limit and suddenly there will be plenty of cards to shuffle again. (This is why every version of Fluxx has Hand Limits.)