Turns out I have called
RESET MASTER; accidentally on the live server. The slaves stopped replication now because they can not find the expected bin log files on the master. Is there a way to continue replication without data corruption and without reimporting the whole dump on the slave?
Is it save to call
CHANGE MASTER TO... with 'mysql-bin.000001' and position 1 on the slave now, because that is where they should continue, or do I risk data corruption in that case and it is generally preferred to reimport the whole dump and start over?