[Answer]
If you have lost your passport, you should file a report on lost property with the nearest police office and have the certificate of theft or loss of the passport. By submitting to your country's government agency in Japan the certificate, your photographs and identification card (driver's license or alien registration card), you will be able to have your passport re-issued. Since a seal indicating your status of residence should be affixed to your passport, you must bring your reissued passport to the Immigration Bureau in your area and have the seal transcribed to it. In some cases you may obtain a travel permission or a travel affidavit instead of a passport
[Answer]
If you are in possession of a Re-entry Permit, the first port of call is
the nearest Embassy or Consulate General of your home country so that you
can have a new passport issued. Of course your new passport will not have
the Re-Entry Permit or Japanese visa stamps. Therefore on returning to
Japan you will be unable to prove your residential status. If you wish
to enter Japan with the same visa status, get in touch with a friend or
relative in Japan and have them apply for a Proof of Alien Registration
Certificate. They then need to take this to the Japanese Immigration Bureau
and receive a stamp proving that you have the required Re-Entry Permit.
If the person assisting in Japan is not a family member than a letter of
attorney will be required. When reentering Japan present your new passport
and Proof of Alien Registration Certificate to the immigration officer.