"Don't dig yourself into a hole" when somebody says something they shouldn't have, is the closest I can think of. Or "When you are in a hole, stop digging" If somebody is trying to rectify a slip of the tongue and then by explaining it, makes it worse
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Mr. TomIf you dig a hole for others, you're sure to fall in it yourself.Actually, your literal translation works quite well in English. I think you may have just invented a new saying, if it doesn't already exist!
Mr. TomIn this context both
PS: What's more natural - there is or there's?
In Brazil we say: The more you wiglle it, the more it stinks".
Don't try to explain a mistake.