to completely finish something that is edible, to completely run out of some kind of food (see Molina)
IPAspelling:
sentɬɑmiɑ
Alonso de Molina:
centlamia. nic. (pret. oniccentlami.) acabar del todo alguna cosa comestible. Alonso de Molina, Vocabulario en lengua castellana y mexicana y mexicana y castellana, 1571, part 2, Nahuatl to Spanish, f. 18r. col. 1. Thanks to Joe Campbell for providing the transcription.