It's reasonably common that a family owned business creates a foundation and places shares in this foundation, to ensure that future ownership remains in the family, and to use the foundation bylaws to regulate voting power within the family.
It's also reasonably common to have a charitable foundation, which is entitled to some of a given company's profits, and then gives away these profits to worthy causes.
Another possible use of foundations is takeover protection, i.e. placing a number of shares in a foundation, and using the foundation bylaws to ensure that a 3rd party cannot acquire a majority of a company's shares.
None of this implies that the government will give you free money.
You can of course request grants and donations from well off benefactors. If these are given to a foundation with is approved as charitable and working for the betterment of mankind, then the people giving these donations may be entitled to a tax deduction.
I don't think this is feasible for regular startups, because:
- A foundation which simply owns a company and doesn't do significant charitable work should not be approved as a charitable, and would not gain tax-exempt status.
- Most startups will not find any donors who will give them donations.
Disclaimer: I'm not a lawyer, this is not legal advice, and you should go see a real lawyer about this.