Some programs have completely rigid deadlines, some only require that the application form is received by the deadline and others use the deadline as a general guide for when the applicants should send in materials. Of course, every program states that the deadlines are absolute. However, the behavior of the admissions committees suggest a more flexible approach. Anyone who gets their application materials into the program before the committees make a final decision will have their application considered by the committee. There is no program that wants to arbitrarily reject an applicant simply because their materials were late.
All programs have a method to receive and deal with late applications.
However, after the acceptance decisions are made, the committee is obviously unable to consider more applications. Programs vary considerably in how they handle the late application. If a program receives hundreds of applications, then the program probably has no flexibility with the deadline. The committee may well end all consideration of applications that are not complete by the deadline. The number of applications to such programs is already large and unmanageable and this policy keeps the numbers down.