Often Tsa Tsas are consecrated by a respected Gurus and monks. To consecrate a Tsa Tsa, the lama presses a finger or palm print into the wet clay on the back while reciting a mantra.
Once the “blessings" are done, the spirituality and wisdom of the master passes to the Tsa Tsa. Such consecrated Tsa Tsa’s are rare compared to the thousands produced for filling stupas, statues and in the caves. Such consecrated tsa tsas are considered valuable asset which is why it is also burned [not just dried] to preserve them permanently.
History says that the Tsa Tsa fell into the wrong hands during the Chinese occupation of Tibet in the last century. If the former owner had fled Tibet, he would certainly have taken it with him.