You do it by breaking up the potentially destructive changes so you could rollback your deployment to the previous working version. Typically all destructive modification of the schema is done in several passes: eg. in each release/deploy:
# copy the data in a new table and add code to place it in both tables
# change the code to reference only the new data but still store it in both tables
# rename the old table
# remove the old table
On top of that you have changes that are supposed to be applied before the new code is deployed (eg. creating a table, renaming a table) and after the code is deployed (eg. dropping unused columns).
As somebody else mentions in the comments this is more about Change Control than Versioning, but the two things go together to insure that you have as much idempotent and reversible changes as possible. Of course, if you have the resources you can always adopt a "never delete data" policy, so you're always copying instead of modifying the data, making sure you have a way to retract the changes. Clean-up can be done on regular, distant intervals.
Using ORM doesn't prevent you from doing a review on the changes that are about to be implemented. ActiveRecord for example, could provide you with a SQL file that will be representing your schema after the ORM is done. Usually the ORM schema changes are executed automatically by your CI upon deployment on Dev, QA and possibly Staging environments (you do have at least two of those, don't you? :) and need manual intervention (maybe to control performance degradation of your live env - locks, increased disk I/O, etc). This way you get plenty of testing of any DB changes and you should be able to spot any problems as early as possible.