Mishnah Pesachim 1:5:
וְעוֹד אָמַר רַבִּי יְהוּדָה, שְׁתֵּי חַלּוֹת שֶׁל תּוֹדָה פְסוּלוֹת מֻנָּחוֹת עַל גַּג הָאִצְטַבָּא. כָּל זְמַן שֶׁמֻּנָּחוֹת, כָּל הָעָם אוֹכְלִים. נִטְּלָה אַחַת, תּוֹלִין, לֹא אוֹכְלִין וְלֹא שׂוֹרְפִין. נִטְּלוּ שְׁתֵּיהֶן, הִתְחִילוּ כָל הָעָם שׂוֹרְפִין. רַבָּן גַּמְלִיאֵל אוֹמֵר, חֻלִּין נֶאֱכָלִין כָּל אַרְבַּע, וּתְרוּמָה כָּל חָמֵשׁ, וְשׂוֹרְפִין בִּתְחִלַּת שֵׁשׁ:
Further did R' Yehudah say: There were two disqualified loaves of a Todah placed on the roof of the portico. Whenever they were placed, the entire people could eat. One was taken, they hang: they don't eat, and they don't burn. Both were taken: the entire people would begin to burn. R' Gamliel says: Chullin was eaten all the fourth hour, and Terumah all the fifth, and they would burn at the beginning of the sixth.
I assume the connection between eating and spontaneously combusting is that the people would begin to fast in preparation of their imminent demise. But why would they suddenly burn in the first place? Was there a way for them to protect themselves, so that they would survive the ordeal?