Legacy code, improvement task that are not finished

Until now I was involved in several projects that contained a lot of legacy code. On each project of this type people tried to improve the code, refactoring it and so on. I think that all of us know this story.
Having a code base with 3 million lines of code or 10 millions lines of code will contain a lot of crape. The code improvement action will never finish, this action will continue until the end of the project (end of maintenance phase) or end of the world.
It is very easily to find problems in a code that was not written by you. In cases like this you can propose a solution. If the architect or the person that is responsible on the project will accept your proposal, sometimes you will have allocated time for this task. We can have one, two, ten or more improvement tasks that run in the same time – assigned to different team members.
But what is happening when an issue is discovered and you receive a phone call from the client with a 911 problem? You will put the improvement task on hold. The same thing can happen when you have a backlog, you start working to the improvement task, but something happens and you have to put the task on hold.
Putting a project on hold is not a problem, but forgetting an improvement task that is partial done can generate an uglier code that you think so. In this case the “forgetting” term don’t refer only to the developer that forgets about the task itself. For example we can have a case when the management will not allocate team anymore for the given task.
In cases like this it is important to look over the changes and decide what you should do with the changes that were already done on the given task. Letting the changes in the code will not be all the time a good approach. You can end up with method, classes or functionality that is not used or with code that do the same thing in two different ways. When a new developer will come on the project and will look over the code he will not know what is happing there - people code and go, we are agile.
Developers will try to improve the code, having 100 great ideas how code can be improved and will start 200 task of code improving in the same time. What is important, when you start a task, you should also finish it. Starting a lot of improvement tasks without finishing them will increase the “legacy” part of the project.
Be prepared to fight for the improvement task. The code should add value to a project (functional/non-functional), it is not only developer fad.