Thank you for your post.
The file structure for FileMaker Pro 9 and FileMaker Pro 11 are identical, so there should not be any compatibility issues between the two versions.
FileMaker Pro 11 is more strict with damage in a file. That is, FileMaker Pro 11 may find errors in a file where FileMaker Pro 9 won't. I would therefore run a Recover (File menu) on the database file using FileMaker Pro 11, and then use the Recovered file with FileMaker Pro 9.
Please let me know if you continue to run into difficulty.
Both versions should be compatible, though features unique to FileMaker 11 won't work in 9. They both use exactly the same file format as well.
Most likely guess here is that your file is damaged with some latent corruption that FileMaker 9 "tolerates" but causes crashes in 11. Try running a recover from FileMaker 11 and see what is reported. Even if no problems are reported, test the recovered copy to see if you still get crashes in FileMaker 11.