What do I do if my part-time master's program is changed to full-time? I am stuck in an unusual situation. I was admitted to a part-time master's program. The classes were supposed to be held in the evening and the expected degree duration was 6 years. 

After only one year, the graduate school decided to change its policies, and abolished the part-time master's which meant that all classes were now held in the morning. Needless to say this, this made it very difficult for people like me who were doing a full-time job in the morning, to continue their master's. It became really difficult to adjust classes in such a way to cause the least interference with my work shifts, and I could not afford to leave my job.

Four years forward, i have managed to pass almost half of my courses, but my grades have suffered heavily due to unattended classes and missed assignments.

I am also quite dissatisfied with the quality of teaching and the general environment of our department. The teachers seem disinterested, there is general mismanagement and very little scope for research, not to mention almost no research funding. 

My questions are:

1.) How common is it for gradate schools to change policies like this? What can a student do in such a situation?

2.) If I decide to drop out from this current program and decide to apply to a more accomplished program abroad (now that I have some savings), how could I explain the unfinished master's and the bad grades in my application? Would the previous unsuccessful stint in Master's hurt my chances of being admitted to a reputable graduate program?
1) I have no answer for this one.

2) Pretty much the same way you explained it to us. Your seem to have legitimate reasons for lower grades and/or dropping out. If you decide to apply for graduate programs abroad make sure to explain this in your statement of purpose. Take your time to word it perfectly. It can make all the difference. The fact that you committed to a six year graduate program while working a full-time job shows passion and dedication. You want to make sure that comes through in your statement.