I have a hard time to imagine how that works out. After all they are not interested in buying any shares so they have to quickly sell everything they buy effectively canceling the buy. How does that provide liquidity?
At any given point in time, the "true" (buy-side) investors are likely to be relatively far apart on prices. This is especially true in thinly-traded markets. For example: consider housing, which is the canonical example of an illiquid market.
I know the value of my house (it's around $300k). Say I want to sell it. The more liquidity I need, the worse price I'm going to get. Anyone with any intuition for the housing market knows that if I have to sell my house tomorrow, I am going to get a god-awful price for it; the "tomorrow" price for my house is many tens of thousands of dollars off its true value.
This creates huge problems for homeowners. The obvious standard advice for sellers is to wait patiently for the best price, counting on many weeks or months before a reasonable offer arrives. But I have to pay money every month I hold on to the house. If I need to move immediately, for instance for a job, or because my financial circumstances have changed, I might need the house to sell quickly, and because houses are illiquid I have to accept a crappy price. Or consider trends in the market: by forcing me to hold the house for months rather than days, I'm maximally exposed to swings in the market. So if Chicago housing prices crater while I'm trying to sell, the extra time it takes to unload the house takes that price swing out of my hide.
(You can easily see how the same thing happens in reverse in "hot" markets like Palo Alto, with the buyer now assuming the role of the hapless Chicago seller).
The exact same thing happens in the public markets; it's just not as intuitively obvious because we're working in smaller deltas of time and price.
But the public markets have a huge advantage that the real estate market doesn't: market makers.
Imagine if houses traded (were bought and sold) so frequently that a smart company could make good educated guesses about the current value of any given house. Imagine if that company would on any given day snap up a house offered for sale. That company wouldn't pay my asking price for my Chicago house, but it would pay something much closer to it than the "true" market would. After buying my house, the company would immediately offer my house for sale at any price greater than what it bought the house for. I wouldn't care, though: either I'd be thrilled for the opportunity to sell my house quickly and painlessly, or I just wouldn't accept their offer and instead do what I do now, which is to wait for the best offer.
Assuming the housing market makers were smart, the money they'd get by forcing me to accept a lower bid would be "free money" they get simply by being smart about valuing houses and having capital available to deploy. We'd all be a little irritated at them for scalping distressed buyers and sellers. But something else will inevitably happen: other smart firms will smell the free money, and they will compete for it. To capture a share of the premiums, all they have to do is offer a slightly more favorable price, so that's what they'll do. Over time, the money the housing market makers will get less and less "free", and the price penalty for immediate liquidity will get lower and lower.
In my fantasy real estate market, I now have the opportunity to avail myself of a reasonable "market" order, or to buy or sell on a "limit" price. I could do that if there were housing market makers, but in their absence I can't, because the price hit for selling tomorrow is too great; it might be a 25% discount on my asking price, or even something close to 50%. That's the cost of illiquidity, or, stated more directly, the value of liquidity.
It's probably also worth saying that liquidity is a presumption of the public electronic markets. Because it's taken for granted, there are whole trading strategies (hedging, for instance) that depend on its presence. These trading strategies face execution risk: if they can't bail out of a position within a specific window of time, they incur losses for the trader.
(It is because of comments like these that I have your comments page bookmarked the same way I would a blog.)