To Egypt
In the first century BCE, the Roman Empire conquered Egypt. Like the Hellenes before them, Roman settlers embraced many aspects of Egyptian culture, including mummification. Such was the vogue of this burial practice in the first century CE that there was a widespread shortage of cloth. The price of cloth rose sharply, and corpses were wrapped in anything available (one has been found wrapped in a sail).
The community that owned the Liber Linteus would have taken this opportunity to make some money from their old junk, and we may yet thank them for it.