Does it happen in the market (if yes, how often) that all the shares of a company have been held up so that there are no more shares to be purchased.

I admit I am new at this and trying to wrap my head around the whole trade thing. I will however try to explain my query.

Let us say a company ABC which went public and declared say a total of 100 shares at IPO. What I believe going ahead only these 100 shares are available for trading at exchanges (unless the company intervenes again and split the share or introduce more, whatever...).

Now my question is, say the company ABC is a great company and everyone wants to keep its share. Lets say 100 persons, (100 different, unknown person; not counting groups or firms here who intent to buy the company by occupying all shares) manage to get 1 share each. Since the company is good none of these 100 investors are willing to release their share. This means all the shares for ABC are held up.

What if I ( as 101th investor) also want to get share of ABC company. What I believe is now I have to wait for at least any one of those 100 to release his/her share. Is it correct or there exists any other way.

If its correct, how often does it happen ?