An example of this is the double negative. "I don't know nothing", which should, of course, be either " I do not know anything" or "I know nothing". There are areas where this usage is endemic and no amount of teaching has managed to erase it, probably because the child may well understand the teacher whilst in school but surrounded by everyone else outside school using the double negative will fall back into that regime.
Be careful, here. Double, and even triple, negatives have always been a feature of many -- probably most -- dialects of English; they're just not a feature of Standard English, which is what is taught in schools. Standard English is used on formal occasions, dialect on informal occasions, and there's actually nothing "correct" or "incorrect" about dialects: merely "appropriate" and "inappropriate" use (e.g. when writing a business letter or a newspaper report). What's happening is not that the children are wilfully abandoning the "good rules" taught in class, but are becoming (hopefully) bilingual within their own language.
This, though, is why I think some kind of grammar should be taught to ESLs, rather than letting it develop "spontaneously", because they may conflate different registers and produce a kind of hybrid mix, which would sound uneducated in a formal setting, and just plain weird in an informal setting.
But it's probably possible to disguise the teaching of grammar to a certain extent. For example...
OK, folks, now, last time we talked about using "will" to make promises: "I will get back to you on this", "We will send the goods first thing tomorrow"... But sometimes, you need to put a condition on that promise. Well, to make a condition, we just take a simple sentence, like "You send us the specification", and put an "If" in front of it, and add it to the promise: "If you send us the specifications, we will make an offer".
And in one easy step you have taught the so-called "first conditional" without ever saying "conditional" or "modal auxiliary".