Courts almost always have very specific rules for calculating deadlines that vary considerably from one court system to another.
In the U.S., the court document usually has a date of mailing at the bottom of the last page under a heading entitled "certificate of service", or a signature date if it is from the court, and the date on that document is usually the date that you count from. Days are usually counted from the day they are sent rather than they day they are received.
Also, sometimes days means calendar days, and sometimes it means business days, an issue which is set by court rule.
If you can't find a date of mailing on the document, you can call the clerk of the court involved if it came from a court, or the attorney sending the document if it was sent by an attorney, to find out what the date of mailing is. Sometimes, for example, the last page of a multi-page document accidentally doesn't get into the envelope due to clerical error.
If the deadline is missed, the person is still responsible unless they promptly file a motion with the court requesting that the deadline be extended after the fact or the late filing be excused. Usually, relief is only available then if there is "excusable neglect", which is a very high standard (e.g. you were in the hospital or kidnapped or there was a hurricane that caused you to be away from your home), although, again, court procedures and local practice may vary considerably. Also, relief is usually unavailable if, for example, the case is an eviction case and the eviction has already happened.