I know of fully expendable Big Dumb Boosters, as well as "smart" reuse in systems like NEXUS (all versions) and their contemporaries, what I'm trying to figure out (after hours of sorting through astronautix etc.), is whether a system of passive full reuse has ever been seriously considered. I ask specifically because the benefit of Big Dumb Boosters are their material cheapness and expendability, and the benefit of reuse, as with SpaceX, Delta clipper, nexus etc. is their cheapness due to not having to build a new one. It seems plausible to me that a reusable liquid fuelled multi-stage pressure fed etc. etc. etc. rocket would be very, VERY cheap. Thanks
It is probably impossible to have a true Big Dumb Booster that is re-usable.
The first issue is that the recovery hardware moves away from the 'dumb' part since any concept with recovery can be made simpler/cheaper by removing the hardware. Starship first stage might be described as a BDB modifed to support recovery, noting it uses a lot of the BDB concepts in design - is it still BDB?
The second complication is that the simple/cheap/overbuilt design assumptions of BDB reduce payload fraction. If the plan is to re-use the rocket making it 10% heavier but 10% cheaper means you pay the payload penalty every flight, but only save the build cost once. At least some cost increase/weight reduction would seem useful if re-using - is this still a BDB then?
That said, it appears the Sea Dragon proposal did include recovery via airbags into the ocean presumably leveraging the fact that pressure fed engines need robust tanks anyway, and the design already needed to be sea worthy enough to reach the launch site. Unlike the scaled up but known elements of Sea Dragon it is notable that the study specifically calls out that:
the technical feasibility of a completely passive recovery system has not been demonstrated.
So the answer of the question as written is that yes, there has been a system described as Big Dumb Booster that also included a recovery/reuse system but it is unclear if it would have worked while still being a Big Dumb Booster - the experience re-furbishing splashed down shuttle boosters suggests they may have underestimated the challenges in 1962. If nothing else passive/distant splash down requires maintaining a large blue water fleet at thousands of dollars an hour that would put limits on even perfect re-use savings, especially if flight rate is low.