In Malaysia it’s common to see “buy one free one” offers in supermarkets, pharmacies etc. I’m a speaker of British English and this construction hurts my ears, but apparently it’s perfectly idiomatic in Malaysian English. I think it’s understood as “buy one and one is free”, although it could that be “buy” is being used as an adjective (one bought, one free), or that “free” is being used as a verb (buy one, get-free one). What linguistic tests could I use to investigate these possibilities?
No doubt someone who knows Malay is needed to give a full answer with the likeliest possibilities, but I'll throw in my speculation while we wait.
I would lean towards "buy" as a verb and "free" as an adjective, with an elided "get":
buy one → (get) free one
In the first place, notice that even in the standard English "buy one get one", we need to parse it with at least one elided link between the cause and effect. In fact, to make a full sentence, a lot of elisions are needed:
(If you) buy one (then you will) get (another) one (for free).
The structure in the Malaysian variant could be read similarly as focusing on cause (buy one!) and effect, the latter being reduced to the noun phrase rather than the verb phrase (hey, a free one!).
It wouldn't be unthinkable to drop a verb like "get". Like existence, possession, and equation, it seems to serve more as the glue between themes than a true action, and could behave oddly in different languages.
We'll have to await our Malaysian-speaking linguists to confirm whether this is a valid hypothesis given typical Malay structures!
Perhaps counterintuitively, providing more complete information often leads to a more negative interaction, as it requires smaller lettering for the same size sign, may take longer to read, etc.
To me, this looks like a reasonable simplification to convey "buy one, get one free". The sign meaning being understood at least locally the same way in the United States "Drive Thru" means that there is a path and window by which you may order from your vehicle.
You could employ the empirical Method and *ask a native speaker how they parse it. If all are in agreement about it being odd, stop looking. Otherwise, you have something to go on.
You can brood force an answer by trying all possible syntactical structures and compare to known specimen of each structure from a known good set, be it BrE or better Malayan. A cross reference with Malay syntax wouldn't hurt either. It does sound a bit Vietnamese broken German 'ish to me, at least.