Games don't have to choose between making resources either plentiful or scarce. No resource has to be supplied in steady stream throughout the game -- be it ammo, mana, health, gear, or other.
My religion, like others, includes an annual time of fasting. For forty days, we make especially difficult sacrifices to remind ourselves of our reliance on God. A game's players can similarly be called to fast; to go without something they normally have access to. The fast can be forced, encouraged, or merely suggested. The player might even be given the choice of what to sacrifice. There's a variety of possible benefits.
The general idea of a fast has been implemented many times before, but I believe there's still plenty of room for innovation.
The most common form of fasting in games is temporarily forcing the player to use a particular weapon or category of weapons. Bioshock, for example, occasionally removes the player's guns so that plasmids must be relied on exclusively. Many shooter games remove players' preferred weapons from time to time.
Another form is lack of aid resources. Left 4 Dead's AI director sometimes makes first aid kits unavailable to increase difficulty.
The form of fasting I find most compelling is reliance on persons or characters. This might be more common in games than I can recall right now, but I'm sure much more exploration is possible.
As in my religious example, such reliance might be constant throughout one's experience but reinforced in a particular moment. People tend to ignore what they are used to, so the momentary emphasis is important. For example, the player in Deus Ex is constantly dependent on NPCs to understand the what's going on (the plot), but it's not until the player realizes he has been lied to or manipulated that he becomes actively aware of that dependence.
A couple shooter games I've played included moments when the player's wounded character is firing at enemies while being dragged by an NPC ally. Left 4 Dead is fully of dependency caused by temporary inability (such as being pinned beneath a Hunter).
What other forms might fasting take in games? and to what purposes?