I don't think I understand what you mean here.
If they buy back shares, what is it you imagine they do with the shares other than add them to the pool of purchasable shares?
If I own shares in a company, I'd be very pleased if they buy back all shares other than mine! $$$$$
Generally, the shares are canceled - this is why remaining shares are more valuable. You have a pie being cut into fewer pieces. Some companies will take the repurchased shares, not cancel them, and add them to "treasury shares" - you will see this identified in the lower part of a company's balance sheet. The shares are no longer in the float, are still outstanding, and may be resold in the market at a later date to raise capital.
In general, there are a number of (big) issues with share buybacks.
1. Over the past few years, many companies have been issuing debt to have the cash to repurchase shares. The theory being that with interest rates low, it makes sense to issue the debt. The debt may be at an interest rate that is lower than the dividend yield - so using debt could be a good move. Additionally, interest paid on debt is tax deductible to the company. Personally, I don't think this should be allowed. Interest should be deductible only if the debt is for operational purposes - not financial engineering in repurchasing stock.
2. Companies which use cash to repurchase shares are essentially admitting that they do not have any operational use where they can get a better return. That's pretty sad.
3. Cash that is used today for repurchasing shares is cash that is not available tomorrow for operational purposes. How awful must it be to have a company you're invested in do big share repurchases when the shares are high, and then a few years later find themselves in bankruptcy? One of the best examples of this is Aeropostale. They did a $1B share repurchase at an average price of something around $16/share. As many folks know, it was just a year or two ago when they were filing for bankruptcy protection. Not that the ultimate outcome would have been any different, but certainly the company could have survived much longer and had more opportunities to turn things around if they had the $1B cash available as opposed to having repurchased all the stock and watched it go to $0. They torched $1B - and that was $1B of profits - no debt used.
4. More times than not, the companies are repurchasing shares not when they are low looking to take advantage of a period of weakness, but rather when the shares are high, and looking to keep them high. More times than not, when the buybacks end, the shares ultimately fall when the artificial demand is removed.
So, to summarize my view - buybacks get a lot of publicity and are most always called a good thing. However, the investor should consider the potential consequences of the company doing the repurchase and if they may be leaving themselves vulnerable if they go through a rough patch. Are the shares being repurchased to take advantage of the market not properly valuing the shares? Or is it the case that it is being done when the shares are at/near all-time highs looking to push them higher?
Tread carefully.