Can They Sue Me If I Don't Serve Notice Period

I worked with this company for 1 week.Due to some family issues i had to resign.But wasn\'t able to serve the notice period of 2 months.So they didn\'t gave me any relieving letter.But they haven\'t even given me any appointment letter.I only signed on some terms and conditions which doesn\'t say anything about notice period or anything.I talked to the HR and mailed my resignation but they didn\'t reply to it.Can they sue me for not serving the notice period.

Dear Jake,
What did the policy for exit during Probation say ? Did you have an access to the employee handbook ? It states the HR Policies and the processes to be followed.
If you know anyone, who is still working in that firm, please get your doubts clarified.
You said you were not issued any appointment letter. How were you notified about your joining?
Even though you served only for a week, please settle your exit with the firm. Send them a registered letter stating your resignation and the communication that you had thereafter.
Looking forward to hear from you.

When you don't have an 'Appointment Letter' from the company & have resigned within 7 days, on what basis are you claiming a right to get a Relieving Letter? For all purposes, you may have been given a chance for self learning, to adapt yourself to the work environment & confirm if you will like to continue. Your resignation can give an impression that you did not feel comfortable & thus preferred not to continue. Where is the question of giving you a relieving letter when you were not yet on the rolls of the company? Please reconcile & join some other company where you can work without looking for a change.

It may be a mistake to think that your employer is a fool & you can manage things to your advantage without being dedicated to your job. Any legal minded person who guides you to the contrary may only be having some business interests. Please do not get into that trap & do not waste your time. Focus on building your career. Take this advice, if you like; my good wishes are with you.