Are you old enough to remember the 1930s?
The theme is heavy handed about how tough life is for convicts trying to go straight. Would it really be that difficult to find some sort of job as a convict? It seems that there would be no real easy and fast way to find out if a person had a criminal record, and that he would be able to find some sort of low level job without his criminal record being verified.
It also seems unlikely that the owner/manager of the trucking company would have given Eddie a job in the first place, and then be such a capricious prick to him later. The directer could have made it look more realistic by showing Eddie knowingly taking a risk of being late or some other low level infraction before getting fired. The way it was portrayed, he was fired more out of spite than wrongdoing.