Assessments in the classroom

We can discuss at length if standardized testing or teaching to a test is right or wrong but I have begun to think of assessment in another way as well.
To me assessment has really become a question of how can a measure if my students have learned what I have been teaching? And if they haven't, what do I do about the problem?
Most of the time teachers (and I have been guilty of this as well) will give a test and to a group of students and almost every time there are few students out of a hundred (give or take 50 ha ha depending on your class size) that do not pass the test. On a standard test we would say that they are "not proficient". Most teachers then go on with the unit and chalk it up to the student not doing enough homework, studying, or something else. What if you looked and saw that the student in question did do all of their homework and you know they studied because they came in multiple times for extra help, what do you do now? Sure you could retest them in another way - but what if they still fail? Most teachers do not have time to reteach a lesson until everyone passes that lesson. So how does reality meet proficiency?