In my young day, there was even an accepted safeword if you needed to check out of a chase-game temporarily for some reason, e.g. you were about to trip over your undone shoe-laces and wanted to tie them up. This, according to the Opies on the Lore and Language of Schoolchildren, had many regional variations: in my part of the country it was 'faynites'.
We could use the "time out" signal from American football and call "Time out!" (we were in America's Heartland) to temporarily halt the game. Even if it looked like chaos, we had devised controls.
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Except for Freeze Tag, where I could the the benefactor if someone were already frozen, and escape ("no tag-backs!").