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All of these things are at a constant hot temperature.
If a pig (or substance used for idolatry, like Yayin Nesech or idolatrous water) falls (or is intentionally placed) into one, can you drink or cook with the water? Are utensils made from the lava kosher?
Leaving the issue of shishim aside, because obviously one pig would become batul (chametz would be a different story, ע"ש), there is a fascinating Shach in Yoreh De'ah siman 94 s"k 22 (see also siman 103 s"k 18) where he explains that taste - which, for background info, normally becomes irrelevant for kashrus after 24 hours of lying dormant - which is reheated within 24 hours will have it's "pagum clock" restarted. Based on this, the taste of a pig which fell in to a volcano would never become batul as long as the heat of volcano doesn't disappear for a complete 24 hours. Although, this probably wouldn't stand, because the heat of the lava would probably incinerate the taste to the point that it loses its status of taste (see S"A O"C 442:1).
