There doesn't seem to be much data on what happens when you drive LEDs under their rated current. I'm reasonably sure that the lifetime curve would be exponential, but any real-world tests, even with 5mm LEDs, would probably take years. For example, extrapolating data at higher currents to lower currents tells me a 5mm white LED which lasts for 6,000 hours at 20 mA would last for about 10,000 hours at 10 mA, and based on the equations lifetime seems to asymptomtically approach ~15,000 hours at very low currents. However, other data I've seen and common sense suggest it might be much longer than that. For example, I've heard that running 5mm whites at 5 mA on a board with fat traces for heatsinking can result in lifetimes of hundreds of thousands of hours. I'd say offhand that the data at high currents can't be extrapolated to low currents. I know I don't personally don't run white LEDs at >10 mA in any device where I need long lifetime.
Low current data for power LEDs would be even harder to come by. As it is they last long enough at rated current to make gathering real world data time-consuming. For example, I have a test Q3J Luxeon running at 350 mA for over 41,000 hours and I haven't measured a decrease in brightness over the last 3 years (didn't have a light meter before then). Based on this, I'd say underdriving power LEDs to 100 or 150 mA could very well result in lifetimes exceeding a century.