In fall, 2008, the US banned short selling of certain stocks.  It triggered a massive short-covering rally.  Then, without the shorts in the market, prices went into freefall.  When prices are falling, the shorts (when taking profits) are the only bidders.  Markets don't crash because of short sellers.  They crash because the bid is withdrawn.

Every time governments have tried to manipulate markets and impede price discovery, it's always had the same disastrous result.  And yet today, several European countries have announced bans on short selling.

My prediction is that, after a possible massive short covering rally and possibly piling-on by momentum chasers, whatever securities are not shortable will collapse.  One reason for this is that a ban on short selling tells would-be buyers that there is something wrong.  And they should withdraw their bids.  Then gravity will take over, as first one seller needs to sell "at the market" (i.e. on the bid) and there is no real bid.

I wrote the following in response to a friend's Facebook post.

First, contrary to popular misconception, the purpose of the stock market is not to go up, ratcheting higher and never lower. Its purpose
is price discovery. This is because it allocates capital, and just as it is important to allocate more capital to the most productive
enterprises, it is equally important to deprive the least productive enterprises of more capital (which they are destroying). Short selling
is a key part of this process.

Second, unlike long buying, short selling tends to be done by more sophisticated investors. With long buying, there is a limit on one's
potential loss but no limit on the possible gain. Short sellers face the opposite: a limited gain and unlimited losses. This tends to make
them more careful, more selective, and to hold positions for much shorter periods of time.

Third, short sellers keep everyone else honest. When people can act free from negative consequences or downside, they tend to become more
and more aggressive and take risks. Imagine if I said go into the casino, and if you win keep it. But if you lose, I will pay you back.
This is also called "moral hazard". Greed is one of the two motivators for market participants. People want to make lots of money. Fear is
the check on it. People really want to avoid losses. Short sellers can inflict losses when people become overly, irrationally greedy.

Fourth, short sellers will tend to dampen volatility. The higher a price goes above its fundamentals, the more short sellers will be
attracted to come in to the market. Perhaps more dramatically, when a market is plunging, short sellers may be the only bid in the market.
Consider how a real market works. Forget "the price" of something.  There are always two prices: the bid and the ask (offer). The bid and
the offer are made by different people, motivated by different forces.  And there are asymmetries. Since money is the most liquid, most
trusted thing in the system, it's never bad to sell an asset and get cash. So there is never a case when the offer is withdrawn. But the
bid is a whole different story. The bid is withdrawn under crisis or stress. This causes a market to plunge, and thus more bids are
withdrawn. Short sellers, on the other hand, have a natural tendency to want to take profits. And thus buy back the shares they shorted.  And thus put in a bid.

Fifth, markets are driven by arbitrage. If the price of copper goes down, an arbitrager can put on the following trades simultaneously:
buy copper (long) and short a copper mining company. If two similarly situated companies are trading at a stable ratio of share prices, and
one's price suddenly starts to collapse (assuming that it's not caused by anything real) the arbitrager can buy the fallen shares and short
the shares of the other to bring the spread back to normal. There are endless examples of arbitrage, which involve at least one short "leg".