なくしてしたそうだ
無くしてしたそうだ
nakushite shita sōda

Conjunction
Evidential Auxiliary

Expresses hearsay about a past event ("I heard that...") of なくしては

1. Without it, they did it.; Apparently, they did it without it.

Past/Perfective
Hearsay Evidence
Usually Written in Kana