My saved files were corrupted due to an energy crash, and I almost lost hope (Steam does not detect any problem with Dosbox files, but they are corrupted). However, I recovered all my files, and here is what I did.
At the directory where your game is installed. There are these files:
C:\Program Files (x86)\Steam\steamapps\common\Phantasmagoria 2\Phant2\

P2SG.CAT
PS2G.000
PS2G.001
PS2G.002
PS2G.003..

All these PS2G.00X are your saved files. And it seems PS2G.CAT is the index for those 00X files. This index was corrupted for me, and it may be for you. Now do this:

0) Copy all PS2G.00X files to another folder and delete PS2G.CAT;
1) Uninstall or delete the game;
2) Download and install the game again;
3) Start a new game;
4) Save as many files as you have (it can be done wherever at the beginning of the game; it doesn't matter). This will create new PS2G.00X files and a new PS2G.CAT.
5) Now quit the game and replace all new PS2G.00X files with your old ones while keeping the newly generated PS2G.CAT.
6) Restart your game again et voila, you are done.

All your saved games are back. Their names changed to the new ones you used, but the progress is there. There is no need to start the game all over again, just load the game from wherever you were. Thank me later.