Last chance undies is your last pair of clean underwear¹, reminding you that this is your last chance to wear any unless you get your laundry done. (Source: urbandictionary.com)

应急内衣是指你的最后一套干净的内衣，穿上这套内衣就意味着“如果你不想裸奔的话，你得赶快洗衣服了”。

For example:

Dude, I gotta do laundry today. I've got my last chance undies on!

哥们，我今天得洗衣服了，我已经把我的应急内裤穿上了。