YOU SAID:
My cat has perished on the basement floor while I was cleaning my wife
INTO JAPANESE
妻を掃除している間、私の猫は地下階で死にました
BACK INTO ENGLISH
My cat died in the basement while cleaning my wife
INTO JAPANESE
地下室で妻の掃除中に猫が死んだ
BACK INTO ENGLISH
My cat died while my wife was cleaning in the basement
INTO JAPANESE
妻が地下室で掃除をしている間に猫が死んだ
BACK INTO ENGLISH
My cat died while my wife was cleaning the basement
INTO JAPANESE
妻が地下室を掃除している間に猫が死んだ
BACK INTO ENGLISH
My cat died while my wife was cleaning the basement
That didn't even make that much sense in English.