You can access the cloud from any computer/phone, etc. if your personal device or devices go down as long as you know your ids and passwords. The solution is to do what you probably would do anyway: replace the device, then log into your accounts and get access to the cloud.
When I say 'any' device, what I really mean is any "cloud" compatible device, for instance 'android' phones or tablets could access Google cloud, apple devices could access apple cloud.
What I don't know is whether there is an easy way to transfer data from an apple cloud to a google cloud. I'm just getting up to speed on this cloud stuff... I'm reasonably sure Microsoft and other computer/software vendors have their own versions of the "cloud" out there, too.