There are ways to do this, but it is hard -- it takes a lot of work both in hardware and software to get a system that is functional, powerful, and low power.
Maybe a good example to think of is the Amazon Kindle. According to this page:
http://www.devicespecifications.com/en/model-cpu/92752e19It has an ARM Cortex-A8 class CPU, yet lasts for weeks or months on a charge.
Those specs list 256 MB of RAM. Thats enough to run Linux, although I don't know what the Kindle does. Of course this will be some low power ram (LPDDRX takes much less power in "suspend mode"), but even that doesn't get you the kind of lifetime the kindle has. Probably it uses a combination of techniques: a low power microcontroller that can take over some tasks without waking the application processor, and an OS optimized for instant-on so that it can go into a super-low power mode that shuts off RAM refresh, yet recover quickly when the user demands it. Many (most? all?) ARM application processors have the ability to configure the CPU cache as an SRAM that you can execute from. This can allow you to have a minimal execution environment for simple tasks without powering up the DRAM.
So these techniques can all limit the standby power, but remember that all of the code that runs in the MCU, or is executing from cache in the APU don't have the benefit of the full Linux environment. As you move more and more of the everyday functionality into those reduced power enviornments, you are going to wonder if it is actually worth the trouble to have the applications processor at all. I am the guy who thinks it is silly how people like to use tiny microcontrollers in non-power and space constrained applications, then faff around with 1980s style C, and then worry about running out of their 8K of RAM when they could just use a bigger processor and written their code faster and more functional. But battery powered application processors are hard.