I have to submit my research proposal and I am very confused from where to start writing my proposal. Which type of methodology should i use in the Research Methodology section. And is there any solution to maintain undocumented code?
Sounds like you'll maybe want to do interviews / questionnaires with people who are dealing with undocumented code. Perhaps trace what's happening over time in source code repositories (how much change is committed to parts of the coder base that is well documented vs. those that are undocumented?). So open source projects are probably a good start. I've worked in commercial environments where lots of coder were essentially undocumented but it may be hard to find people who are willing to speak openly about those examples, let alone hand over repo access.
Concerning solutions, in my experience any undocumented / poorly documented code is best maintained extremely defensively (don't touch it unless you absolutely have to) and by adding documentation as you go.
There's also the opinion that 'the code is the documentation' but that only works at the fundamental level and definitely not beyond a certain layer of complexity, and in any case that only shows you what the code does and not what it is supposed to do (ie. what should be bugs and unintended side effects become features).