Burying a case means that police do not follow up on a report by a citizen, but simply treat the report as never having existed. Or, a major case may be reported as a minor case.
「吃案」是警政機關對民眾所報案件，沒有持續偵察、往上通報，反而當成案子沒有發生，產生所謂「匿報」或「大案報小」的情形。