Sometimes these are not real "job offers" but a goodwill gesture to assist trainees in bad times.

Some firms can't afford to retain as many trainees as they wish to but don't want to put them out to dry. So it's basically - you can continue hanging around the office at a really low pay until you find a full-time position elsewhere. In the meantime, you can take off for interviews as and when you like and no notice necessary. If you find something, go ahead and accept.