So far as I can tell, science grows more powerful in each of two different but interrelated ways.
1. As the experimental data come in, the theories must change so that they accurately predict the results from an ever wider set of experimental circumstances.
2. Occasionally, there is a theoretical improvement that both increases the range of predicted circumstances and simplifies at some level the overall conceptual framework.
So long as civilization does not altogether collapse, and the various scientific communities along with it, neither of these two senses of scientific accomplishment depends on funding, but the rate at which science becomes more powerful does depend on funding.