I know it's a silly question before I ask but let's ask it anyway:
Let's say that X buys 10 shares of a public company Y in the stock market.
Let's also assume that Y, at some point, goes bust while X still owns the 10 shares.
Can X, along with the other shareholders, be considered liable for the debts accumulated by Y?
No. One of the key ideas behind a corporation is that an investor's liability is limited to the amount he invests, i.e. the amount of stock he buys.
This is the primary reason why small businesses become corporations, even though one person owns 100% of the stock. Then if the business goes broke, he won't lose his house, retiretment fund, etc. He'll lose everything he had in the business, but at least there's a limit to it. (In some countries there are other ways to achieve the same results, like creating a "limited liabililty company", but that's another story.)
No, assuming by "public company" you mean a corporation. The shareholder's individual liability is limited to their investment. Your shares can go to zero value, but that's the limit.
EDIT
In regard to the follow-up question in the comments: "Are all companies in the stock market corporations?" the answer is definitely "no." I cannot say much about other countries, but the US markets have some entities which are known as "master limited partnerships." These trade shares on the market by the usual rules, but if you buy you become a partner in the company rather than a shareholder. You still have limited liability in this case, but there will be differences, for example, in how you're are taxed.
The answer depends on whether the company involved has 'limited liability'. Most, but not all public and listed companies and corporations have this, but not all so it is worth checking and understanding what you are getting involved with.
The expression 'limited liability' means that the owners (shareholders) of a company have a liability up to the amount of the face value of the shares they hold which they have not yet paid for. The difference is usually minor but basically it means that if you buy $10 of shares you have no liability, but if the company gives you $10 of shares, and you pay them (in cash or kind) $5, then you still have a liability of $5. If the company fails, the debtors can come after you for that liability.
An 'unlimited liability' company is a different animal altogether. Lloyds insurance is probably the most famous example. Lloyds worked by putting together consortiums to underwrite risk. If the risk doesn't happen, the consortium keeps the premiums, if it does, they cover the loss. Most of the time they are very profitable but not always. For example, the consortiums which covered asbestos caused the bankruptcies of a great many very wealthy people.
Not normally, for a limited liability company anyway. In extreme circumstances a court may "lift the veil" of incorporation and treat shareholders as if they were partners. If you are an office bearer or a director that is found to have breached duties/responsibiities then that is another matter. Dim views can be taken of shonky arrangents for companies formed for activites not of a bona fide business nature too.
I am a tax lawyer and ALL the RESPONSES ABOVE are 1/2 Correct but also 1/2 Wrong and in tax law this means 100% WRONG (BECAUSE ANY PART INCORRECT UNDER TAX LAW will get YOU A HUGE PENALY and/or PRISON TIME by way of the IRS!
So in ESSENCE ALL the above answers are WRONG! Let me enlighten you to the correct answer in 5 parts, as people that do not practice tax law may understand (but you still probably will not understand, if you are NOT a Lawyer). 1) All public companies are corporations (shown by Ltd.), 2) only Shareholders of Public companies (ie, traded on the NYSE stock market) are never liable for debts of a bankrupt company, due to the concept of limited liability. 2) now Banks may ask a sole proprietorship (who wants to incorp. for example) to give collateral, such as owners stocks/bonds or his/her house, but then of course the loanee can tell the Bank No Thanks and find a lender that may charge higher interest rates but lend money to his company with little to NO collateral. 3) Of course not all companies are publicly traded and these are called private companies. 4)"limited liability" has nothing to do directly with subsequent shareholders (the above answer is inaccurate!), it RELATES rather to INITIAL OWNERS INVESTMENT in their company, limiting the amount of owner loss if the company goes bankrupt. 5) Share Face-value is usually never related to this as shares are sold at market value in real life instances (above or below face-value), or the most money Investments Banks or owners can fetch for the shares they sell (not what the stock's face-value is set at upon issuance). Never forget, stocks are sold in our Capitalistic System to whomever pays the most, as it is that Buyer who gets to purchase the stock!
In an open corporation scenario a stock holder may well be found liable. It's a very narrow and uncommon bunch of scenarios but it's well worth sharing. See the paragraph on open corporations in the following document: http://nationalparalegal.edu/public_documents/courseware_asp_files/businessLaw/RightsOfShareholders/LiabilityOfShareholders.asp