Is it permissible to inform the family of the prospective bride about the true nature of the suitor’s work after his acceptance based on false information, or is silence obligatory as long as one has not been asked?

You must inform the girl's family about the reality of the suitor's job, even if you are not consulted, as long as you know that they would not accept him if they knew; because this is part of the obligatory advice (naseeha). Advice is required for those consulted or not consulted in such matters, just as a buyer must be informed of a defect in merchandise.