When the Tabernacle was dismantled, the offerings were immediately disqualified. This refers to the most holy offerings. Furthermore, offerings can be eaten in two places, both in place of encampment and while traveling. This must refer to the regular holy offerings. Thus, the most holy offerings cannot be eaten without the Altar, but the regular ones can!
However, Abaye found for himself support from a different teaching: Rabbi Ishmael says that the offerings cannot be eaten without the Altar, but the Sages says that they can - and Abaye follows the view of Rabbi Ishmael!
Alternatively, said Abaye, the "second place" where even the most holy offerings can be eaten is the time when the Levites took down the curtains. You might think that having no curtains is the same as taking the meat outside the Courtyard. It's not! - and you may eat the sacrifices without the Temple standing.
Art: Joseph Mallord William Turner - Shade and Darkness