I'm a freelance web developer, and I have a client I'm currently making a website for. I'm in the final stages of the project, with only some rough minor details left to attend to before I would normally send in my invoice and conclude my business with the client. While the work left is minor, it's still a good few hours of work, and the current project is visibly unfinished in some portions of it. Unfortunately, my client has had a death of a close family member happen not long ago, and this death has struck my client quite hard both financially and otherwise. As such, my client has informed me that they can no longer afford for me to continue to work on the project.
I'm now torn between what I should do. The client asked me to send in an invoice for the work I've done so far, however I don't want to leave the project in an unfinished state, especially since it's so close to being completely finished. Not only would I feel bad about leaving them with an unfinished product while still getting paid for it, but it's also something I simply couldn't showcase in my resume/portfolio, since an unfinished product like this would send a bad image to people that lack the context of the project.
However, I also can't justify working for free when I have other, paying clients I need to attend to. Likewise, I definitely would not want to put any additional burden on my client in a very difficult time for them. I'd definitely be willing to lower the rate for the last few hours of work, but I feel like that's an inappropriate response to the situation as well.
What is my best course of action here?