Dear Mukesh,
There are various types of leave. Earned leave apart, many companies make provision for "Leave Without Pay" (LWP). When emergent situation arises and when employee does not have any leave balance, he/she can apply for LWP. Therefore, you may talk to your HR and ask for LWP on compassionate grounds. If you are working in the same city where HR is then go and talk to him personally. If the HR is located at some different station then talk to him on phone and explain your problem. Hopefully HR shows temperateness. If HR also shows intemperateness, then you will have no option other than resigning from the job.
As of now you are attending your filial duties. Problems of your kind are common amongst the lower/higher middle class persons. Nevertheless, we have to strike balance between filial duties and career requirements.
From the company side, they are unable to grant any more leave because most of the companies work with lean manpower. There is no provision for standby manpower like in government departments. Hence their inability to extend your leave.
Both the parties have their own perceptions. However, when perceptions differ, situations of this kind arise.
All the best!
Dinesh Divekar