Phrase when you offer someone something but it's really them who are paying for it

In Dutch, there is an idiom iemand een sigaar uit eigen doos geven, which literally means to give someone a cigar from [their] own box. The idiom is used when you offer someone something, but it's really them who are paying for it. The idiom has a negative connotation.

For example, it may be used in politics. Suppose that the government introduces major cuts to some service, then restores a fraction of it and presents it as a gift/improvement. Or suppose an employer increases some particular non-salary benefit to employees, but finances it entirely by reducing employee salaries. Critics may then refer to this as a sigaar uit eigen doos.

Is there a corresponding idiom in English? One online dictionary translates it as something out of one's own pocket, but searching the latter phrase in context does not yield examples where it is used with a meaning similar to the sigaar uit eigen doos.

There should be a comparable English idiom, but there isn't.

If it were me, I see nothing wrong with following the example of (a mere) twelve instances in Google in which a (probably Dutch) author used the English translation of the idiom in an English context.

The idiom, translated as a cigar from one's own box, is self-explanatory enough in my opinion that I would feel comfortable using it without scare quotes or any other apology.

From this link:

It is an impressive amount of technology, but it seems completely operator-driven. To a certain extent, it is a complicated way to serve the users a cigar from their own box!

I think that "give with one hand, (only to) take away with the other" is an expression you can use to refer to the examples you are making:

From : Uncle Sam's Shame: Inside Our Broken Veterans Administration

• At her best she did give with one hand, only to take back with the other, doing one thing then undoing what she did, and so ultimately offering a little, but only what was an approximation of that which was originally ...

From: Interpretation of Statuses

• ... not so construe the provision as to attribute an intention to the legislature to give with one hand and take away with another.

In the business world, you often hear that the definition of a consultant is "someone who borrows your watch to tell you what time it is".