In master, it's impossible to save Budget Plans as there is no save button.
When the budget is locked, the "Save" button disappears from /cgi-bin/koha/admin/aqplan.pl, but you can still interact with the text fields on the page. These text fields should be marked as read-only, and there should be a warning that the budget is locked.
The interface has changed since. It it no longer possible to change values when the budget is locked. bug 26754 adresses the warning. *** This bug has been marked as a duplicate of bug 26754 ***