When you reach the limit, Bugfender will drop any logs that come over the limit. Bugfender will slow down the acceptance from that point on, randomly discarding any logs that go over the limit, to match the amount of logs permitted by your plan.
Of course, you can upgrade to lift your log limit immediately! You can also reduce the number of logs you send to match your limit.
Even if your account is over the log limit, your application will run normally.