I am supposing this will not work - simply using dd to copy the booted disk /dev/sda for example to a file on an external hard drive. This would not be a good back as too many system file would be missed. right?
Is there an easy way to create a very minimal linux that runs out of memory or that would live in a very small partition, that would be capable mainly of dd ing the working partition to a file on a USB?
I think it's good enough. Shut down as many services as possible if you want to be safer. In the end it would just be like booting after a power failure.