It's hard to imagine such a situation. If the price of a single share drops below one cent, it will still not be zero as it would be possible to say it's worth, say, around half a cent if trades are usually around the mark of 2 shares for every cent in an order.

However, let's pretend it is zero. The most direct impact is that financing by equity from public markets is no longer possible as you could issue an infinite amount of shares and not receive a penny for it, potentially diluting all current shareholders. Conversely, you could buy back the entire company for free, assuming there are no liquidity costs.

There are two sides to every trade: a buyer and a seller. For the share price to be zero, the seller would be literally giving away their shares for free. It's hard to imagine any situation in which sellers would be motivated to do that. They might be prepared to sell cheap, but not for nothing.

Let's play out your scenario.

Share price of (near) zero means BUY, BUY, BUY

Remember the golden rule.

I mean the other golden rule: Buy low, sell high. Very important not to mix those up.

It's important that you understand what "low" and "high" mean; that's relatively to the core value of the company. You specified a company with good core value.

Science has proven that a share price of zero qualifies as "low". Therefore, buy like a freak. Dig through your couch cushions for $0 coins. Short your rent check by $0 to buy more shares; your landlord will understand.

Best case scenario: you own the company. Use some of the company's actual assets to hire the best business consultants you can get. Have them tell you how to best "weather the storm".

Emerge from the other side of the crisis with a company with fantastic fundamentals.

Sell.

Why that won't work

If it made sense to do that, others much more attuned to the marketplace with much better research departments would have already done that, and this action would have either privatized the company or raised the stock price back to equilibrium.

Of course if the company is very small, and privately held, this absolutely can happen. Sometimes a small business owner lacks a key skill needed for the business to flourish, and gets sick of failing and says essentially "who will take this business off my hands?" I once could've had a very niche business for less than $100,000. It could've earned $250,000/year in competent management. The reason that didn't happen is the particular set of skills needed to make it work are scarce as hen's teeth.

Functionally negative stock price can actually happen. I've been an employee of a strong company that was ripe for acquisition by a major. However they had, for lack of a better word, toxic debt; a huge mortgage on a 5000-seat building on prime real estate the company had built just for it (they had shrunk to <200 employees). As long as they bore that mortgage, nobody wanted to acquire the company because they didn't need a new 5000-seat headquarters that was upside-down. As things were, they traded most of the company's cash to the builder to get out of the mortgage. Boom! They were acquired a week later.

Depends

For the London Stock Exchange, the price will not go to 0, because a listing requirement for Standard and Premium shares is a minimum market capitalization of £700,000. That is, the stock will be delisted well before the price drops to 0.

For the New York Stock Exchange, the minimum share price is $1, and the minimum capitalization is 1.1 million shares (among other requirements including number of shareholders, etc.). If a NYSE stock falls below $1 for more than 30 days, it will be subject to delisting. Most major stock markets have similar rules.

When a stock is delisted from the major markets, it may continue to trade via so-called Pink Sheets. In the US, these have a minimum price increment of $0.0001, but I cannot find any declaration of an actual minimum price. Given the argument by others that it would be irrational to give away shares for $0, I think it is safe to assume that no publicly traded shares will trade for less than a hundredth of a penny.

Of course, privately traded shares have much fewer restrictions, but again, it does not make logical sense to trade any shares for exactly $0.

Book Value

Note that minimally rational shareholders will never bid a share down to £0 anyway, if it is "still operating and it's far from going bankrupt", as you say. That's because the corporation has assets which can be sold off even in the event of liquidation. As an owner, a shareholder is thus going to value shares up to the portion of those assets to which they are entitled, which is called the book value. This valuation may be below the listing requirements for major exchanges, but again, that seems unlikely for an otherwise healthy corporation.

@timday's answer is correct that a zero share price means that a seller is giving away the shares for free. However, short sales create willing buyers which keep a stock price from dropping to zero, even in bankruptcy:

• A short-seller is basically making a bet that the share price will go down.

• Short-sellers borrow shares and sell them. At a later date (and hopefully at a lower price), they buy back the same number of shares, returning them to the party lending the shares, and keeping the profit.

• A stock that is plummeting will attract short-sellers, willing to bet that the price will drop further. However, they are contractually obligated to buy shares again at a future date.

• A rational seller will always demand at least some non-zero price. As long as there are short-sellers contractually obligated to buy shares, the sale goes through, and the stock price is nonzero.

A real-life example is the bankruptcy of the old General Motors. After Old GM filed for liquidation in 2009, the U.S. and Canadian governments, with several labor unions, funded a completely separate corporation, the New GM. Using the money from this funding, New GM purchased the good assets of old GM at auction (including the GM name itself, other intellectual property, factories, and inventory). This left Old GM with all the debts and liabilities (e.g. creditors, asbestos claims, product liability, environmental damage) and no assets to generate revenue.

Stockholders of General Motors prior to bankruptcy now owned shares in the worthless Old GM (officially called Motors Liquidation Company MTLQQ), and were given zero shares of New GM. Even the website of Old GM warned that the stock had no value:

Management continues to remind investors of its strong belief that there will be no value for the common stockholders in the bankruptcy liquidation process, even under the most optimistic of scenarios. Stockholders of a company in chapter 11 generally receive value only if all claims of the company's secured and unsecured creditors are fully satisfied. In this case, management strongly believes all such claims will not be fully satisfied, leading to its conclusion that the common stock will have no value.

I had 1000 shares of old GM bought at $3, and expected them to be worthless because of the bankruptcy and the public admission quoted above. Nonetheless, I was able to sell them at $0.40 per share. Why? Because there were short-sellers who were contractually obligated to buy the stock, even if it was already worthless.