No, I bin work that is plagarised because it is not the student's work, it is someone elses. Students are told repeatedly that they must not plagarise. They are demonstrated the correct way to quote, how to reference and how to paraphrase. This lesson is endlessly repeated, especially before the submission date for assignments.
Legally, I cannot give marks for work that is not a student's own. So it is binned. If the student feel humiliated by this it is usually because they know full well what they have done and have been caught out. I never bin original work, however bad it is, I mark it with as much care and attention as I can, looking for any way to give marks.
It is not unusual for the least capable students in my classes to gain the highest marks in final assessments. This is because they tend to be the ones who actually listen to instructions and hand in their own work.
I don't have an issue with children with special circumstances. What I have an issue with, borne out of years of experience, is those who use the term as a 'get out of jail free' card. I could give you hundreds of examples, like the student in an external eamination who kept on raising his hand and asking for help then kicked up a tantrum, disrupting 300 other students, wailing "But I've got family problems!", or the one who would cry racism any time any teacher (black, white or any shade in between) gave him a poor mark.