Makaru and mawiru
Here's a Man'yōshū poem (#700) that nicely illustrates the original difference between the Japanese verbs makaru and mairu. The heading is 大伴宿祢家持到娘子之門作歌一首, "A poem Ōtomo no Sukune Yakamochi composed upon arriving at a young woman's gate":
如此為而哉 猶八将退 不近 道之間乎 煩参来而
kaku site ya/ napo ya makaramu/ tikak'aranu/ miti no apida wo/ nadumi-mawi-kite
Just like that, I'm going back after all?—After all the hassle I went to on that non-short road to come here?
A naive hypothesis would be that makaru means "go" while mawiru means "come". The truth is a bit more complex: makaru means "move from a place of high status to a place of low status" and mawiru means the reverse. Here Yakamochi is using it as a politeness strategy, exalting the residence of the poem's intended recipient by comparison with the lowly hovel he has implicitly come from.
In the case of mawiru this usage survives into the present day — mairu is in the standard keigo library as a humble way to express the act of moving to your interlocutor's current location. I don't believe makaru has retained any significant role, though.
Azuma:
There's まかり通る, but I can't think of any other vestigial survivals off the top of my head.