This is next in a series -- "Ten Things I'd Like to Tell Every New Philanthropist." Each title has a statement that paraphrases a common misconception or mistake.
Logically, how does discontinuing funding to a nonprofit make them more "independent" or "less dependent"? There is a reality for most nonprofits -- they depend on funders (corporate, individual, public) for some or much of their revenue. To the degree that they have fee-for-service, or earned income revenue streams, they can become less dependent on philanthropic sources of funding. But discontinuing their funding is not an action that prevents or reduces their dependency per se. If a funder wants to improve a nonprofit's independence and long-term sustainability, they can focus on capacity building, longer-term and bigger grants, investing in outcomes systems, etc.
On a related topic -- sometimes funders/philanthropists will be less likely to give to a non-profit with a strong net asset position, because "they are already financially strong enough and some other org needs my money more." Yes, there is such a thing as too cash rich (e.g., more than 1-2 year's annual budget amount held in net assets), but a non-profit's net assets are its working capital, its investment capital, its buffer against the ups and downs of running any organization. It's not money "just sitting around, doing nothing."