THIS is exactly why we, at the Pilgrim Office in Santiago, always tell people to fill in the front inner page of the credencial. If there is no name or other personal identifying information, that credencial could belong to anyone. - like immediately after getting it
My advice to the person who lost this, if they cannot be reconnected to it soon, is to start another one as soon as they can. Take pictures with your phone. The metadata behind every photo you take identifies where and when it was taken.
If you have a credential that qualifies for the Compostela - having walked at least the final 100 km of the route into Santiago, and establish that with two stamps daily - you could still ask for the distance certificate. You can prove that you started at a location and followed a specific route of march by using photographic evidence on your smartphone.
Over the years, I have seen many pilgrims in this predicament prove entitlement to a distance certificate using photos that they took. Just sayin.
Hope this helps.
Tom