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I am sorry to hear about this situation. To get an extension to file an answer, one files a Motion for Leave. This asks the Court to "take leave" of the rules of procedure for good cause, i.e. in this case, to provide more time to file an answer. The motion has to be drafted, filed, served unto the other party, and set for a hearing.
NOTE that depending on the court and the notice requirements to the other party, the setting to have the motion heard may fall PAST the deadline for the answer. If so, one may wish to file something as an answer, and then to amend it later.
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