Primary or direct Effect: No
Company gets money usually from its share during first time- example IPO. So, even shares fell after that does not have immediate effect.
Drastic fall in share price for long time could hurt promoters or many executives whose fortune is tied to company.
Secondary Effect: YES
When shares fell then investors in the company are those who really get hurt. But it could have some impact on intangible asset like reputation of a company. It also means that public perceive company less valuable.
If company wants to raise more money by issuing more shares then company would want their share to trade high so that they could raise more money.
Swapping of company's share occur when company acquire another company or in case of merger with other company. Here, also value of share price does matter. For larger companies these type of activities are happening all the time.