I grew my eggplant in kitty litter buckets this year and had some overripe like that.. after pale they started turning a golden brown. I harvested them anyway and used them in eggplant parmigiana just fine. The seeds in them were harder, but the taste was not affected one bit with more mature eggplant used.

You can pick the green tomatoes and stick them in a cardboard box and set in your kitchen. They will start to emit ethylene gas, which is what ripens them. I harvested all my green tomatoes the evening before the first frost in my area last year and did this. The tomatoes ripened sporadically in the box for weeks and weeks. We just ate whatever did not rot and what ripened. We ate the last ripened one on Christmas last year. lol