Trending @Infosys; Notice period negotiation

Hi, I need some advice here. I have extensively discussed with my manager regarding early release, but turns out I am not able to get it. I need a release by this month ending, and that would mean me serving 2 months' notice. If I say that I have a family emergency and I won't be able to work for the next one month (ik that it will be a loss of pay), how would that situation turn out to be? Can they extend my notice period?