WARNING: this is a no-edit zone....
Q. My book is coming out and they've just announced that the line/imprint is going to be discontinued. I think this spells disaster for my book, and I don't want to spend any money on publicity and lose more. This has to have happened to other authors. What has happened to their books?
I'm sorry. This is a tough break, but you're right, a lot of other authors have experienced it--and survived it. I can't speak for other authors and their experiences, but I have been in this position twice and I will share my personal experience with you.
In the mid-1990s, I wrote a couple books in a series. These weren't in a line or under a specific imprint, but the books were related and we were forthright about closing out the series. Sales on the last book dropped, and that was expected, but the sell through was terrific.
Now this is a different situation in that the books were related, but I thought I'd pass it along for whatever good you can glean from it.
Just recently, a situation more like yours happened to me. I wrote HER PERFECT LIFE (my personal favorite of all the books I've ever written) and shortly before publication, it was announced that the line/imprint (these are single title novels published in series format) was being discontinued. I worried. Was assured by the publisher that the book would be fine, and I'm REALLY happy to tell you that it's doing well.
It came out in April, and right now it's something like 17,000 on Barnes & Noble, which takes in numbers online but also from its brick and mortar stores. So my personal favorite is doing better than I expected (due to my earlier experience).
How your book will do, I can't say. But I can say that it's been word of mouth that's helped Her Perfect Life. It's grown legs on its own. I know that because I know what I've not been in a position to do to market or publicize it because of the eye surgeries.
So my first advice is to have faith in your work. Then take a look at how the other books in the imprint are doing. Gather as much info as you can on that and then use it as a gauge on whether or not to invest in marketing/promotion and how much to invest.
If you do invest, do lay out a budget--and then stick to it. That's the one thing that gets so many authors into trouble: not sticking to that budget.
Regardless, try not to despair. Both of these situations had positive effects. The higher sell-through was good. The book selling well is good. (And there's an added sense of gratitude in knowing that this book is touching readers as it touched me).
I wish you and your book every success, and I hope this helps!