I understand that if a congregation missed reading a parsha one week, the following week they would read two parshiot - the one missed plus the one for the current Shabbat. (I'll B"N edit in a source for that, later.)
Let's say the shul had one Torah and during the reading, a Psul was discovered in the Torah scroll, so they had to stop the reading in the middle of the Parsha.
What do they do the following week, in addition to reading that week's parsha?
1- Read all of the previous week's parsha? I.e. is the obligation of public parsha reading "all or nothing"? 2 - Read starting from the point they left off the previous week until the end of the previous week's parsha? 3 - Just read the current week's parsha. I.e., even having read part of the parsha that week was fine, bedi'eved.