In social work, doorknobbing is the word sometimes used to describe the phenomenon of delaying the important personal revelations until the end of the therapy session when goodbyes are being said.
This option has the advantage of actually being in circulation. It has the disadvantage that it also carries one or two very different meanings of a frank sexual nature.
I can see two ways to parse the phrase "have him get addicted to drugs", in different contexts.
The first means "Cause it to pass that he gets addicted to drugs".
This matches exactly with "Have him get killed" in the other question, which as I said would be unusual in reference to reality rather than in terms of a writer's relationship to fiction.
Still, it would not be impossible in referring solely to real people, it's just unusual because in circumstances where we could arrange such a thing to happen we would have strong control over they means and it would be more likely to express that as "have him killed".
Now, here we could say "have him addicted to drugs", but the adjective form of addicted is much more common than the past participle addicted so it reads strange for that reason.
We could say "have someone addict him to drugs", but again that sense of addict isn't commonly used. Let's assume that most people wouldn't even think of that sense.
So therefore, "have him get addicted to drugs" is more normal. It's the same usage as "have him get killed" except that there are more normal ways of rephrasing the latter than the former, so the latter is more likely in the special case (relating to creating a narrative) only while there are no such alternative phrasings for the drug case.
There is another possible parsing:
Live with someone for a few years, raise beautiful children with them, then have them lose their job, then have them get addicted to drugs, then have them suddenly become violent like they never were before, and only then would you be able to talk about what you would do if you were me.
This phrase from a (thankfully fictional) speaker who has been through the experience of living with someone who is addicted is putting forward a hypothetical. Here it uses the verb have in its sense of "experience, undergo", in an imperative mood that doesn't make literal sense (they are not suggesting someone actually do this) but could relate to something that does (they are relating it to previous experience).
I'm sure there are other ways to parse it too, as you only give a bare phrase rather than the amount of context you did with the last question.
Best Answer
Let us consider the example of "no less than the country's president attended".
In many countries with the title president, they are of considerable political power. In most of the rest, it is still a position of considerable esteem. As such, there would be few, or no, potential attendees of greater rank.
So, the set of people who are "not less" than the president will be very small; either just the president or else the president and a handful of other people.
To have someone from that small set attend is therefore remarkable.
So, it literally means "someone who ranks as least as highly as the president attended", and the person referred to in this roundabout fashion is indeed the president. You would not expect someone to say "No less than the president attended. It was the Taoiseach who has more real power".
This is a from of litotes where we use an understatement to produce emphasis, often a double-negative or negating a comparison to produce the opposite comparison as in this case ("no less than" meaning "at least as great as").
Litotes is found in many languages, and very common in English. We have "not bad" for "good", "not bad looking" for "attractive", "no spring chicken" for "old", and so on. English has quite the history with it, as Old English poetry used it a lot.
It can perhaps be best read as "Wow, the president attended, can you imagine, the president. That's the most impressive person there could possibly be attending!", but from a more reserved speaker.