If it's the business version, you have full access for 30 days, admins have access for 90 days, then it's deprovisioned (source: https://support.office.com/en-us/article/What-happens-to-my-...)

On the O365 Personal/Home or direct OneDrive plans, it looks like your data remains available but read-only for 3 months, then your account is "frozen." You can do a one-time 30-day "unfreeze" to get access to download/delete (to get under your quota), then it gets "frozen" again. Eventually it'll be deleted, but I don't see documentation for how long that takes. (source: https://support.office.com/en-us/article/what-does-it-mean-w... linked from https://support.office.com/en-us/article/OneDrive-storage-pl...)

I believe the modus operandi for most personal cloud storage providers here is to make the entire dataset read- and delete-only until the user gets enough storage space (by upgrading or deleting files) to be able to write/upload again. That, plus some incessant push messages to your client devices about upgrading, which is annoying but expected.

Office stops working if your subscription ends so most likely they will renew their subscription.