Your files will remain on your account, your account will simply become read-only.
If you're using Docs, this means you can't save anything, or upload anything new,
If you're using Photos, you can't upload any new photos.
Currently, we have no specific cancellation time-policy for accounts that have exceeded their storage quota. However we do have have an abuse detection system.
If you for example get an account, fill it up to 20gb, then cancel your payment, but keep accessing the account for a long while, your account may get flagged after a certain amount of read-bandwidth is consumed.
(There's no set cap, but an organic alert system that would mark your account if numbers are too high), and if the activity continues the system automatically bans the read-access and only the account settings page becomes accessible for the payment.
We've made these restrictions very relaxed, and you will be alright if you're not abusing the system.