If you apply for naturalization (N400) then do not go to interview what happens and you do not receive notice on time?

It depends on why you did not get the notice. If you moved and did not notify the USCIS, then it may be your fault. If you did not move but the mail did not deliver, you can request a new date from USCIS.

By law, every applicant for naturalization must attend and be interviewed. If you fail to appear for any immigration benefit for which personal interview is required, CIS will deny your case for lack of prosecution. If a notice was in fact not sent, you can request a Service motion to reopen. You will not have to pay the usual motion fees. If you cannot show Service error, you can still file a motion to reopen and for good cause, the motion will be granted. You will have to pay for this. A denial for lack of prosecution is not with prejudice and you can re file your N-400 as soon as possible. The ultimate course of action will depend on what makes you comfortable.

It can be deemed abandoned. Do an infopass inquiry to explain why you did not get proper notice and it might be rescheduled. Go to Uscis.gov.

Usually, they'll automatically reschedule you for another day and time, however, to be sure, do make an INFOPASS appointment with the United States Citizenship and Immigration Services through their website: www.uscis.gov and speak to them about what happened.