We all know incomplete problems called wicked problems that usually put the whole architecture concept in its own problem as we cannot follow the usual path. However incomplete solutions are something we all meet much more often as they are often designed to be incomplete such as with minimum viable products where an incomplete solution is often something that answers the problem much better than a complete solution. In case of a MVP we therefore always need to ask ourself if we are really aiming for a complete solution.
Also from a scientific angle incomplete solutions are often preferable as in some instance the work required for a complete solution is just not feasible. Also for pure mathematical logic scenarios we have to acknowledge the Goedelsche incomplete theorem and as such the solution is either wrong or incomplete and as such incompleteness becomes desirable.