Is it moral to propose work that's already partly done?
Let me make two points. The first is that in order to write a research proposal you have to understand the area well enough to describe it. This implies that you have already explored it and have done some work to get it ready for submission. Even after you submit, you aren't likely to just forget about the problem until you get funding. The alternative would be just saying random things in research proposals. So, there is no alternative, in my view, to making proposals on partially done work. 

The second point is at the other extreme. I've heard that some very successful researchers, though the stories may be apocryphal, work like this. Do research problem A. After you are nearly done, write a grant request for problem A and if it is funded, write the report but use the funds to do problem B, that wasn't mentioned in the grant request. If B is successful, write a grant for it (B) so that you have funding for problem C, etc. 

You might question the ethics of this, but the realities are that the funders get what they funded, and the researchers get the funds they need to do research that the funders (and society) like. If you think about doing it any other way, what you wind up with is a lower success rate for funded research (hence less funds for students, etc) and lower reputations all around. That is because there is no guarantee that your initial thoughts on a research topic will bear fruit. So you try to solve more problems than you can reach conclusion on. Lower "success" doesn't serve anyone very well and turns research into a sort of jungle - eat or be eaten - situation. 

But, I'll also note that if you apply for a grant for a piece of work and tell the funders that it is nearly done, you won't get funded. That should be pretty obvious, I think. On the other hand, if you ask for funding for a wild idea you just had, you won't get funded (unless you are already a superstar). So there is a tension here. So maybe there is a sort of "sweet spot" in which it all fits. But certainly the work is partly done before funding is contemplated by either the researchers or funders. 

Even if the real situation isn't quite as extreme as this, a researcher funded for A and working on A would be foolish to completely ignore problem B if it occurred along the way. S/he would be wise to follow the threads for at least a while to see what potential there might be. People, including researchers, aren't machines that work on only one thing at a time to the (mental) exclusion of all else. 

The reality is somewhere in between these extremes, though both extremes exist, I'm pretty sure.