Companies also have treasury stock. And if they issue new shares, the going price will be that (although dilution occurs).
The market cap still holds as it doesnt matter whether a company or mom and dad hold shares.
If you own a house for $1M entirely, but then split the house 50/50 with a family member on paper so you both own it. You each own $500k. But the house is still worth $1M.
They can issue new stock but shareholders don't generally like that. Microsofts outstanding shares have only declined recently for instance...
Microsoft shares outstanding history from 2006 to 2021. Shares outstanding can be defined as the number of shares held by shareholders (including insiders) assuming conversion of all convertible debt, securities, warrants and options. This metric excludes the company's treasury shares...
Buybacks etc are more common than new shares being issued.
Either way once issued the stock belongs to the buyer...not MSFT and the value is irrelevant to daily business. They cannot buy anything with shares held by other people or institutions